Hydrolox isn't very good on Earth, but:
- Out of all possible lunar ISRU fuel options, hydrolox seems to be pretty available in lunar craters.
- For Terran launchers, hydrolox isn't a good fuel except in stages that operate in a vacuum, already having been sent on a suborbital/orbital/escape trajectory, where it's one of the best fuels, and in circumstances that don't involve the hydrogen sitting there for long periods of time. However, on the moon it is a different story. Hydrolox might shine here, because the moon's lower gravity and lack of atmosphere means that the low thrust and energy density isn't as much of a problem anymore (and hydrolox upper stages are still better than other fuels, having to build a bigger fuel tank does not offset the higher fuel efficiency of hydrolox). And the increased efficiency means we can work with a 450 ISP first stage (maybe closer to 500 ISP but it depends) rathera measly 300 ISP (even the Raptor engine, using relatively efficient methalox and using a *highly* efficient engine cycle, only has 327 ISP at sea level, and this is sea level optimised, and even with a giant vacuum optimised nozzle this is still only 380 ISP in a vacuum at most). Small changes in ISP can affect delta-v massively, and this is something like 50% more ISP, so imagine what that could do. Launching from the moon is already advantageous enough (according to a Reddit user a Falcon 9 could get the same amount of payload to Jupiter Orbit if launched from the moon as it could get to low EARTH orbit if launched from Earth), and Falcon 9 doesn't even use hydrolox, rather using inefficient kerolox. Imagine using a 450 ISP rocket on a world that has such a low gravity that it allows you to send 20 tons to Jupiter with inneficient kerolox.
Hydrogen is cryogenic. It boils at 272 degrees Celsius. Not gonna work, right? Well, the moon has no atmosphere to conduct heat, and it's frigid anyways in the permanently shadowed craters. On Earth, we have used hydrogen for liftoff stages (plus some high thrust boosters), so on the frigid moon we should be able to keep temperatures really cold. It mgiht be a good idea to have reusable hydrogen first stages that launch, have an second stage (preferably some kind of fuel that can be manufactured on the moon) and maybe some more stages as well, and then return. (It should be noted that it is hard to keep hydrogen cool when the sun is baking your spacecraft, which leads to:
1: Me not suggesting reusable hydrogen second stages or Starshjp-liks hydrolox rockets, as both roles would require the spacecraft to stay in space for a while and by that time the hydrogen would probably boil off
2: SpaceX using methalox and not hydrolox for their Starship. There are other issues too, hydrogen can weaken metal like what is being used to make Starship, as well as hydrolox forcing engine components to operate at 1 degree above absolute zero, and hydrogen leaks easily too, that made them switch to methalox rather early on.