It might be easier to fire the lasers from the moon, but getting the lasers to the moon would be a huge pain.
So it would be awesome to directly pump the laser from H3 fusion.
H3 fusion is actually very easy - I think we could do it today. We just don't have a readily available source of H3 for fuel.
However, 3He fusion with net power output is exceptionally hard, even with complete disregard to cost. Much harder than deuterium-tritium fusion. We don't know how to do it yet.