More specifically, I've had some debates with a friend on how a planet with low oxygen would work. Of course, it's his IP so he insisted on low oxygen, and we're hand waving aspects of it.
But for my own curiosity, does a planet with lots of liquid water on the surface mean it'll have more oxygen? Is there any correlation or is it simply based on how large it is and therefore what it can hold onto?
Would the latent oxygen dissolved into water or something?
In a young planet, oxygen can be produced from water vapor via photodissociation, which occurs along a pathway like $$\text{H}_2\text{O}+h\nu\to\text{H}+\text{OH}$$ $$\text{H}+\text{OH}+h\nu\to2\text{H}_2+\text{O}$$ $$\text{O}+\text{O}\to\text{O}_2$$ In The Atmosphere and Ocean: A Physical Introduction, Wells writes (p. 26)
This gave rise to an oxygen level of 10-4 of the present atmospheric level (PAL).
$\text{O}_2$ would tend to rise, and would have shielded the water vapor (which would have sunk a little, in comparison) from continued photodissociation. Ozone, too, would have been produced, for added shielding, but not yet in amounts as great as in today's atmosphere. So water vapor was a primary source of oxygen in the atmosphere, and thus planets with more liquid water at the start would likely yield more water vapor, and thus more oxygen. However, this can only get you so far (though objections about the absorption of photons by atmospheric oxygen has been questioned; c.f. Brinkman (1969)).
So, why do we have so much oxygen today - 10,000 times as much as was produced abiotically in a young Earth? Well, it's from photosynthesis, beginning with the Great Oxygenation Event over 2 billion years ago. At the earliest stages, this occurred with extremely primitive creatures living in a narrow band near the top of the oceans, deep enough that they were shielded from harmful radiation by high enough that light still penetrated the surface layers (i.e. a band between a few meters and 30 meters below the surface).
This leads to a sort of feedback cycle, if organisms that can use oxygen later develop, creating an Earth closer to the one we live in today. Increases in photosynthesis led to more atmospheric oxygen, and cells evolved to use that oxygen, making the cycle grow more and more.
A planet with a lot of water (H$_2$O) has the potential for a lot of O$_2$ (and O$_3$) in its atmosphere, but that is not a complete picture of the planet's composition.
The atmosphere of Venus has almost all of its atmospheric oxygen bound up in carbon dioxide (CO$_2$) and sulphur dioxide (SO$_2$), the two composing 96.5% and 3.5% of the atmosphere respectively. Sulphuric acid (H$_2$SO$_4$) clouds also temporarily hold the oxygen not yet lost to space. The lack of a strong magnetic field means Venus has lost much of its atmospheric hydrogen, helium, and oxygen to atmospheric escape, leaving heavier elements to bind oxygen.
So your friend's planet may be an Earth-like world transitioning to a young Venus, perhaps as the sun's luminosity increases as our own has. Or it may be like late-Hadean Earth, with open oceans but relatively little free oxygen due to a heavy CO$_2$ atmosphere. In either case it would have to be a geologically active planet to explain the carbon and/or sulphur in the air.
Unfortunately an atmosphere that high in CO$_2$ and SO$_2$ would be hostile to human life, and the acid rain (thanks to the aforementioned H$_2$SO$_4$) would be hostile to basic life forms. Presumably your friend wants people walking around without pressure suits or breathing masks, among grassy fields and lakes that won't dissolve their skin.
