It's a commonly held misconception, but you really don't need a lot of gravity to retain an appreciable atmosphere. Conversely, gravity alone is no guarantee that a body will have an appreciable atmosphere. There is a lower bound which is dependent on atmospheric composition and temperature, but it's not that high. Wikipedia has a handy chart of escape velocity versus temperature and what this means for the ability to retain various gases; it shows that by gravity alone, at a temperature of a warm 300 K, you'd need an escape velocity at the surface of about 5 km/s to retain an oxygen/nitrogen atmosphere.
jamesqf has already mentioned Titan which, as per Wikipedia, has a surface gravity of 1.352 m/s2 (less than that of Earth's moon) and an escape velocity of 2.639 km/s (about half of what you'd need to retain an oxygen/nitrogen atmosphere at 300 K as per Wikipedia's chart linked above), yet a surface atmospheric pressure of almost 147 kPa (over 1.4 times that of Earth). Now compare this to Mars (3.711 m/s2, 5.027 km/s, 0.4–0.87 kPa) or Venus (8.87 m/s2, 10.36 km/s, 9 200 kPa) and you can easily see that there is no simple, direct relationship between atmospheric density and surface gravity. Other factors dominate. For comparison, Earth has an atmospheric pressure of 101.325 kPa (international standard atmosphere), a surface gravity of 9.807 m/s2 and an escape velocity of 11.186 km/s.
Addressing the (good) point made in comments that the low temperature is what allows Titan-as-we-know-it to hold on to so much atmosphere, that may very well be a part of the explanation for how Titan can hold on to its atmosphere, but it can't be the entire explanation for what is required for such a body to hold on to an appreciable atmosphere, or Venus would realistically have much less atmosphere than it does in real life. Note that I'm discussing using Titan for inspiration, not as the full answer.
Once you have a rocky body that is able to retain an appreciable atmosphere and has moderate gravity, the ability to support even Earth-like life pretty much comes down to just atmospheric composition and temperature. Titan is, again, slightly on the chilly side, but I don't see any reason why a Titan-like rocky body couldn't exist closer to its host star with an atmospheric composition more similar to that of Earth, which would result in a warmer climate.
Try putting a Titan-like, slightly more massive and possibly smaller (both of which will increase surface gravity), rocky moon in an orbit around real-life Mars or Venus, both of which would support landings (the only thing making Venus particularly difficult to land on is its noxious atmospheric composition); add some oxygen and carbon dioxide to its atmosphere (which is almost entirely nitrogen, at over 95% by volume; to match Earth, you want that down to about 80% by volume); and you'll probably be pretty close to what you need. As a bonus, adding the oxygen to Titan's atmosphere will also almost certainly get you a little bit of water vapor when the oxygen reacts with the hydrogen and methane in Titan's current atmosphere, which should itself help warm it up a touch — water vapor is one of the most potent greenhouse gases around. Titan has a few percent methane and around 0.2% H2, which, when it reacts with oxygen, should give you somewhere on the order of a percent or two water vapor by volume, which is comparable to that of Earth. All you'd need is to add some 25% oxygen to the existing atmosphere and let chemistry and (Earth-like) life do the rest.
You can also give the moon an active, liquid core and thus a magnetic field, which will help it retain its atmosphere over astronomical time scales. Orbiting a massive planet should help here by introducing tidal effects.
And if you're willing to stretch the definition of "moon" a little, also compare the masses of Pluto and Charon; the latter is so massive that the two can more accurately be described as a double-planet system than as a planet and a moon. (Technically, the barycenter of the Pluto–Charon system lies outside of Pluto, meaning that the two orbit a common point between them, rather than Charon simply orbiting Pluto.)
There's no real reason why such a moon can't orbit an uninhabitable planet. While a bit of a stretch for your specific question, consider that Europa orbits Jupiter; while Europa is at least semi-potentially inhabitable by hardy life, Jupiter is squarely uninhabitable.
Hence, really, no significant handwaving required.