I'm pretty sure there's distinction between lucid dreaming during REM sleep and something akin to day dreaming while falling in and out of sleep, which some might still call lucid dreaming. I've experienced both. In the latter you won't feel refreshed in the same way (or at all), similar to when stress or alcohol prevents restful sleep. (Stress or alcohol very well may have setup the conditions for the non-REM dreaming.) In the former you feel the same as you normally would.
