A world where there are trees would have to have a dense atmosphere, probably mostly nitrogen, with at least a little carbon dioxide and a little water vapor in the atmosphere, and also oxygen in the atmosphere. Even though green planets release oxygen into the atmosphere, they also need oxygen in the atmosphere. And of course any humans in the story, or aliens with requirements similar to those of humans, or large animals with requirements similar to those of humans, will need significant amounts of oxygen in the atmosphere.

The original question depends on two different factors or aspects of the gravity of the fictional world.

One is the surface gravity which determines how much things on the surface weigh. The other is the escape veloctiy which determines how slowly particles escape from the upper atmosphere into space, depleting the atmosphere.

A world with a dense atmosphere will have to retain that atmosphere for billions of years for that atmosphere to gradually become breathable for humans and other large multicelled oxygen-using animals, as photosynthasizing plants gradually produce enough free oxygen in the atmosphere.

Obviously for a story set on a world signicantly smaller than Earth which has a dense and breathable atmosphere and life the writer may try to make the surface gravity as low as possible while making the escape velocity as high as possible, while also making each of those factors scienticially consistent with the other.

And the formulas for calculating escape velocity and surface gravity are different.

https://en.wikipedia.org/wiki/Surface_gravity[1]

https://en.wikipedia.org/wiki/Escape_velocity[2]

As a result, for terrestrial type worlds more massive than Earth, the surface gravity is higher, relative to that of Earth, than the escape velocity is relative to that of Earth. And for terrestrial type worlds less massive than Earth, the surface gravity is lower, relative to that of Earth, than the escape velocity is relative to that of Earth. Which is very fortunate for writers of stories set on worlds smaller and less massive than Earth.

And the difference might be increased by changing the average density of the materials which terrestrial type planets and moons are made of in a fictional solar system, so that it is different from that of terrestial planets in our solar system. By changing the average density of a world's materials a writer might be able to increase the difference between the surface gravity and the escape velocity of a fictional moon by a bit. But not by a vast amount, because there are strict limits to the density of materials that a world with a solid surface can possibly be made of.

Most discussions of planetary habitability discuss habitabilty for any type of Earth life at all. And some types of Earth life flourish in environments on Earth where humans would die almost instantly, such as several kilometers high in the atmospehere, or below the surface of the ocean, or even deep within rock underground. So no doubt many worlds which would be habitable for lifeforms similar to some lifeforms on Earth would not be habitable for other lifeforms on Earth, such as humans.

As far as I know the only scientific discussion of the habitability of planets for human beings, or for other large multiclelled Earth animals who have environmental requirements similar to humans, is Habitable Planets for Man, Stephen H. Dole, 1964, 2007, which writers of stories set on other planets should study.

https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf[3]

On page 53 Dole establishes an upper mass range for a habitable planet, one where the surface gravity is 1.5 g, corresponding to a planet with a mass of 2.35 Earth mass, a radius of 1.25 Earth, radii and an escape velocity of 15.3 kilometers per second - which is 1.367 times Earth's escape velocity of 11.186 kilometers per second. Note that these factors all have different values realtive to Earth.

Dole says the lower limit on mass for a habitable planet depends on its escape velocity compared to the root-mean-square velocity of the gases in its atmosphere. According to table 5 on page 35 if the escape velocity is divided by the root-mean-square velocity of a gas, the ratio shows how long that world can hold that gas in the atmosphere.

If the escape velocity is equal to one, or two, times the root-mean-square velocity of a gas, the world will retain that gas for basically zero time. If the escape velocity is three times the root-mean-square velocity of a gas, the world will retain that gas for a few weeks. If the escape velocity is four times the root-mean-square velocity of a gas, the world will retain that gas for a few thousand years. If the escape velocity is five times the root-mean-square velocity of a gas, the world will retain that gas for about a hundred million years. If the escape velocity is six times the root-mean-square velocity of a gas, the world will retain that gas for about forever.

The root-mean-square velocity of a gas depends on its atomic weight and its temperature.

On page 54 Dole estimates that the smallest planet capable of retaining atomic oxygen in its atmosphere for long times would have an escape velocity at least five times the root-mean-square velocity of atomic oxygen in the exosphere at the lowest temepratures likely on a habitable planet. That comes to 6.25 kilometers per second, or 5.269 the escape velocity of Earth. That comes to a planet with 0.195 the mass of Earth, a radius of 0.63 Earth radius (and thus a diameter of 8,036.28 kilometers or 4,993.51 miles), and a surface gravity of 0.49 g.

But Dole believed that such a planet would be too small to produce a dense oxygen-rich atmosphere. In the next few pages Dole calculated that the minimum mass necessary to produce a breathable atmosphere would be either 0.25 or 0.57 Earth mass, and then rejected both masses. Dole decided that the minimum mass necessary for a planet to both produce and retain a dense oxygen-rich atmosphere should be between 0.25 and 0.57 Earth mass, and settled on about 0.40 Earth mass. That would correspond to a radius of 0.78 Earth radii (and thus a diameter of 9,938.76 kilometers or 6,175 miles) and a surface gravity of 0.68 g.

Of course there have been many advances in planetary science since 1964 including using computers to model the formation and history of planetary atmospheres. So it is possible that someone has sused such computer modeling to calculate the minimum mass of a world capable of producing an oxygen rich atmosphere. And maybe that hypothetical calculation indicates that the minimum mass of a planet capable of producing an oxygen rich atmosphere would be higher than 0.40 Earth mass, or maybe that it would be lower than 0.4 Earth mass.

In any case a writer can have a oxygen-rich atmosphere on a planet with a mass as low as 0.195 Earth mass if they state that the atmosphere was not formed naturally but produced by an advanced civilization that terraformed the planet and gave it a dense, oxygen-rich atmosphere sometime in the past.

So a planet or moon could have a dense oxygen-rich atmosphere with large lifeforms on it with a mass as low as 0.195 Earth mass, which Dole calculated would correspond to a radius of 0.63 Earth radius (and thus a diameter of 8,036.28 kilometers or 4,993.51 miles), and a surface gravity of 0.49 g.

If a small planet or moon had a surface gravity of about 0.5 g, some people might estimate that trees on that planet could grow as much as twice as tall as trees on Earth.

I don't know how accurate such an estimate would be, but we can go with it for a while.

Two main opposing forces affect a tree's height; one pushes it upward while the other holds it down. By analyzing the interplay between these forces, a team of biologists led by George Koch of Northern Arizona University calculated the theoretical maximum tree height or the point at which opposing forces balance out and a tree stops growing. This point lies somewhere between 122 and 130 m (400 and 426 feet),[41] a range that includes the height of the tallest reliably-measured tree, a 126 meter Douglas Fir.[42][43] On the one hand, the researchers found, trees in forests "desire" to grow as tall as possible to overtake neighboring trees and reach stronger sunlight. On the other hand, gravity makes it more and more difficult to haul water upwards from the roots to the canopy as the tree grows, and leaves thus become smaller near the top. They discovered that despite the moistness of the ground far below, the leaves at the treetops struggle to get enough water, so they are effectively living in a constant drought. The difficulty of getting water so far up into the sky is what ultimately constrains growth.[44]

https://en.wikipedia.org/wiki/List_of_tallest_trees[4]

A naive interprestation is that a world with half of Earth's surface gravity might have trees reaching a maximum height twice as tall as the tallest trees on Earth. Thus the theoretical maximum possible height on that world might be about 144 to 260 meters, or about 800 to 852 feet.

Of course there are stories about trees on Earth that were taller than the theoretical maximum height, but those might just be "tall tales".

For example, among the mountain ash (Eucalypsus regnans) of Australia, a few taller than the theoretical maximum height have been recorded. One in 1867 was measured at 132.9 meters or 449 feet. The "Robinson tree" measured in 1887 was 143 meters or 470 feet tall. The fallen "Ferguson Tree" measured in 1872 was 132.6 meters or 435 feet long to where the top had broken off. The tree was still one meter in diamter where the top had broken off, so some people estimate the "Ferguson tree" could have been up to or over 152.4 meters or 500 feet tall!

http://natural-environment.com/blog/2008/01/22/tallest-tree-ever-recorded/[5]

So maybe the heights of those trees were inaccurate. If the heights of those trees were accurate, maybe the estimate of the maximum possible height of trees is slightly too low. Or maybe some species of trees have some sort of special adaptation which enables them to rise water to greater heights and wasn't considered by the scientists in their calaculations.

Of course if Luna, the Moon, had a dense and oxygen-rich atmosphere trees might grow even taller than 800 to 1,000 feet there. The Moon has a surface gravity of 1.62 meters per second per second, or 0.1654 that of Earth, so trees could potentially grow up to 6.04 times taller on the Moon, or to maximum heights of about 2,400 to 3,000 feet according to a naive guess that the maximum height of trees would vary directly with the surface gravity.

But the Moon doesn't have a breathable atmosphere. It would be possible to give it a dense and oxygen-rich atmosphere through a massive terraforming project, but how long would that atmosphere last?

On page 54 Dole estimated that a planet with Earth-like temperatures at the surface could have a temperature as low as 1,000 degress Kelvin or 1,340.33 degrees Fahrenheit in the outer exosphere, where gases escapedfrom the atmosphere. Thus atomic oxygen in the exosphere could have root-mean-square velocities as low as 1.25 kilometers per second.

The escape velocity of the Moon is 2.38 kilmoeters per second, which is 1.904 times 1.25 kilometers per second. According to table 5 on page 35, Dole calculated that an escape veloctiy only one or two times the root-mean-square velocity of gas molecules would result in a world losing its atmosphere more or less instantly.

But it has been suggested that someone could build a roof over a planet or moon and then introduce an atmosphere under the roof. Air supported roofs have been built so such a giant world-covering roof could be supported by the pressure of the air underneath it. So if the Moon was terraformed to have a dense atmosphere under some kind of roof trees could grow on the moon as tall as the lunar gravity and the height of the roof allowed.

But Titan, the largest moon of Saturn, has a dense atmosphere despite having a surface gravity and escape velocity similar to that of the Moon. The atmosphere of Titan is 1.45 times as dense as Earth's atmosphere, being 97 percent nitrogen and 2.7 percent methane. That is very impressive considering the surface gravity of Titan is only 1.352 metres per second per second, 0.835 times that of the Moon, while its escape velocity is only 2.639 kilometers per second, 1.11 times that of the Moon and 0.236 that of Earth.

With an escape velocity of 2.639 kilometers per second, the root-mean-square velocity of nitrogen in the exosphere of Titan should be less than one fifth of that, or 0.5278 kilometers per second, which can only happen if the temperature of the exosphere of Titan is very muchlower than that of Earth's exosphere.

The surface temperature of Titan is about 94.1 Kelvin, - 179 Celsius, and -290.2 Fahrenheit. The temperature in the exosphere of Titan may be higher than that.

Titan can and does retain large amounts of Nitrogen in its atmosphere. So the root-mean-square velocity of nitrogen in the upper layers where it coudl escape from Titan must be less than0.5278 kilometers per second. Atomic nitrogen has an atomic weight of 14 and molecular nitrogen has an atomic weight of 28, while atomic oxygen has an atomic weight of 16 and molecular oxygen has an atomic weight of 32. Thus any hypothetical oxygen in Titan's atmosphere would escape a bit slower than nitrogen does, so Titan should be able to to retain significant amonts of oxygen for geologic time spans, which L. Dutch said in fewer words inhis answer.

Does that mean that a moon like titan could retain an Earth-like atmosphere at Earth-like surface temperatures? Only if the upper surface of that moon could have a temperature as warm as Earth's while the other atmospheric layers had a surface temperature as cold as Titan's.

If the surface of that moon was warmed to Earth-like tempratures by radiation from its star, the outer atmospehre should be heated up to temperatures like those of the outer layers of Earth's atmosphere. Oxygen and nitrogen molecules and atoms would be moving too fast and would escape far too rapidly.

So the outer atmosphere of the moon should be very cold compared to Earth's outer atmosphere, while the surface and lower atmosphere should be as warm as on Earth, from internal heat sources. And somehow the surface heat has to be prevented from heating the outer atmosphere.

Greenhouse gases like carbon dioxide and water vapor could retain some of the surface heat and keep it from warming up the outer atmosphere. Unfortunately there are limits to how much of those greenhouse gases an atmosphere could have before it becomes toxic to humans and beings with similar atmospheric requirements. It is even possible that too much of those gases might become toxic to Earth-like trees.

A plausible method of heating the interior of a world is tidal heating. A large moon of a giant planet could have a lot of tidal heating from its planet and from any other large moons of that planet. L. Dutch also mentioned that in fewer words in his answer.

Of course there are various scientific limitations of the possibility of habitable exomoons of giant exoplanets in other solar systems.

So writers of stories set on habitable exomoons of giant exoplanets should read scientific articles on that topic.

For example, Rene Heller and Roy Barnes "Exomoon Habitability constrained by Illumination and Tidal Heating", Astrobiology, volum 13, number 1, 2013.

https://faculty.washington.edu/rkb9/publications/hb13.pdf[6]

In Section 2. Habitability of Exomoons, Heller and Barnes find somewhat differen lower and upper mass limits for habitable worlds including exoplanets and exommons, than Dole did. Though I don't know whether they were discussing habitability for humans or habitability for microsopic life forms.

A minimum mass of an exomoon is required to drive a magnetic shield on a billion-year timescale (MsT0.1M4; Tachinami et al., 2011); to sustain a substantial, long-lived atmosphere (MsT0.12M4; Williams et al., 1997; Kaltenegger, 2000); and to drive tectonic activity (MsT0.23M4; Williams et al., 1997), which is necessary to maintain plate tectonics and to support the carbon-silicate cycle. Weak internal dynamos have been detected in Mercury and Ganymede (Gurnett et al., 1996; Kivelson et al., 1996), suggesting that satellite masses > 0.25M4 will be adequate for considerations of exomoon habitability. This lower limit, however, is not a fixed number. Further sources of energy—such as radiogenic and tidal heating, and the effect of a moon’s composition and structure—can alter the limit in either direction. An upper mass limit is given by the fact that increasing mass leads to high pressures in the planet’s interior, which will increase the mantle viscosity and depress heat transfer throughout the mantle as well as in the core. Above a critical mass, the dynamo is strongly suppressed and becomes too weak to generate a magnetic field or sustain plate tectonics. This maximum mass can be placed around 2M4 (Gaidos et al., 2010; Noack and Breuer, 2011; Stamenkovic´ et al., 2011). Summing up these conditions, we expect approximately Earth-mass moons to be habitable, and these objects could be detectable with the newly started Hunt for Exomoons with Kepler (HEK) project (Kipping et al., 2012).

M4 is an abbrviation for the mass of the Earth.

Note that one of the sources, Williams Kasting and Wade, Habitable Moons around extrasolar giant planets, claims that a world could retain oxygen for 4.5 billion years if it had a mass at least 0.07 Earth mass, and could retain nitrogen for 4.5 billion years if its mass was greater than or equal o.12 Earth mass, a significantly smaller mass than Dole's 0.195 Earth mass.

And Heller and Barnes's maximum mass for a habitable world about 2.0 Earth mass, is also smaller than Dole's maximum mass of 2.35 Earth mass.