Personally, I wouldn't stick to the scientific concepts too strongly.
I imagine: if you're dreaming, you could be lucid.

I read LaBerge's book with explanations of the sleep cycles a while ago so I don't even remember exactly whether the REM stage is on the same level but a different stage from delta sleep and whatnot but if that's the case then I imagine that you can be lucid at any stage that causes dreams. When you're dreaming, you could become aware of it.