Not sure, but don't really think so.

Our brain is already more active when we asleep than when we are awake. We dream every night. The only difference I see is, that when lucid, we are aware that the dream is happening right then, instead of remembering it only after we wake up. We catch it in the act, hehe.

And I don't think body uses more energy, since body is asleep same way in lucid or in regular dreams. Anyway, that's what I think.