It can't be any different than a regular dream. The only thing separating an LD from an actual dream is the fact that you consciously know you're dreaming, and I doubt that realization will suddenly prevent you from REMing. I think I know what you're thinking, that LDing is some kind of "awake" dreaming where since you're consciously thinking and making decisions, you're not actually asleep, but that's not true. You're still very much asleep and very much in REM. That's probably one of the big draws of LDs, you can go on all your adventures in real life during the day, then sleep and go on even more while dreaming, all at no cost to you personally.

Almost sounds too good to be true huh? But then again, so do regular dreams don't they?