I'm not sure if this is the convention, but after some more research and reading all these answers I think we may have come to something approaching an answer.
So, it seems we have a number of factors that influence skin colour:
- Original population genetics
- UV exposure
- Vitamin D production
- Sexual selection
- Resource cost of producing melanin
- Gamma radiation exposure
Original population genetics sets the startpoint and pre-existing genetic variety, but we can split the rest into pale-selecting and dark-selecting pressures:
1. Vitamin D production
2. Sexual selection
3. Resource cost of producing melanin
1. UV exposure
2. Gamma ray exposure
From these, for our lunar population we can discount Vitamin D production (in order to protect from UV they'd have to avoid direct sun exposure, so vitamin D would likely be sourced from food). We can also probably discount the resource cost of producing melanin given that it's taken so long for numbats to lose their expensive-to-produce teeth (I'd like to find some other data points for that). Sexual selection is an interesting one, but considering the relative stability of skincolours and lack of sexual dimorphism it's probably pretty weak.
So, it basically comes down to relative exposure of UV on the earth's surface to gamma radiation on the moon. If the radiation on the moon is equivalent to northern Europe we might see a gradual slow movement towards paler skin. If it's equivalent to Africa (or higher) then we will likely see a move towards darker skin (potentially rapidly).
Unfortunately, there's a maddening lack of studies comparing the relative damage of gamma ray and UV exposure. Closest I've come to finding something is a load of people stating how difficult it is to compare them and one guy who's actually done something and found that 6J/m² of UV exposure and 4 Grays of gamma exposure killed the same amount of chicken cells (conditions unknown so not the greatest test but it's all we've got).
From this study we can see that in Europe we are around 200J/m² per day. In central Africa we are around 5000J/m² per day.
The highest figure I can find quoted for average radiation on the lunar surface is 120 millirem per day (others hover around 50 millirems), which converts to 0.0012 Grays of gamma radiation. Practically nothing. Wait, why are we scared of gamma radiation on the moon again? Unless they're quoting shielded figures, or the 6-to-4 ratio of that guy was for one layer of cells (so gets multiplied by each layer of cells the gamma rays reach that the UV rays don't).
The only thing I can see that would be a problem gamma-radiation-wise is the recommended maximum radiation dose for fetuses (50 millirems per month plus the 25 millirems background). So, sod all effect on adults but very dangerous for kiddos, unless I'm missing anything major.
Oh, and apparently during an 18-month study on Mars there were 2 events which saw radiation increase to 2000 millirems per day (0.02 grays).
So, all of that weighs out to a very slight selection pressure towards paler skin with a cultural trait of hiding pregnant women within rad-shielded bunkers, or a strong selection pressure towards jet-black skin in order to protect their unborn children.
Edit: apparently the safe level for radiation exposure in US legislature is 5000 millirems per year, or 13.7 millirems per day. Lower than the level our lunites will be receiving. So, leaning towards the jet black option of the two above...