The principal reason of this question is that I know people that can willingly enter in lucid dream (and so do what they want in it, and wake up when they want). Some of then use EEG (not professionnal one, ZEO sleep manager or Olimex) and they lucid are on NREM2 or REM.
So it's still sleep (the brain waves length are said to be sleep). But they can basically fall asleep and start lucid dream.
Important point to mention: those people are doing polyphasics sleep, hence the capacity to fall asleep for a nap really easily. But because of this they don't try to sleep outside their schedules.
However, the thing is that they relax and then fall asleep in a lucid state.
Meditation can be observed in theta wavelength (Manocha, n.d.; Aftanas & Golocheikine, 2001) (referenced by Wikipedia). But it's mindless meditation.
Also this question refer meditation as a good method to fall asleep.
If you simplify it (a lot) meditation and lucid dream can have a lot of common points.
But is there any known relatio between the two? Is it possible to fall in lucid dream by meditating?
References
Aftanas, L. I., & Golocheikine, S. A. (2001). Human anterior and frontal midline theta and lower alpha reflect emotionally positive state and internalized attention: high-resolution EEG investigation of meditation. Neuroscience letters, 310(1), 57-60. doi: 10.1016/S0304-3940(01)02094-8
Manocha, R. (n.d.). Research Summary: Brain Waves. Retrieved from: http://www.researchingmeditation.org/meditation-research-summary/brain-waves
