Lucid dreaming is not dangerous for health. It has been tested over and over by psychologists like Pr Laberge, Pr Tholey and Pr Zadra they didn’t see anything dangerous in it. It can even be useful in overcoming recurring nightmares.
By the way, your assumption about resting your mind while sleeping is incorrect. REM sleep phases are also called paradoxal sleep cause your brain works as if you were awake. And it seems that LD’ing doesn’t really change the brain activity.