I would think not, but I’ve read in multiple books that it matters. has there been any scientific research done? why should sleeping on your right vs. left make any difference? I can maybe see stomach vs. back because of air flow…but not left or right. maybe certain organs that are only on one side. or is it it more “spiritual” like chakras or something…what do you guys think? mainly I want to know if any real studies have been done. I don’t see why it matters
For me, my sleeping position doesn’t affect my lucid dreaming. It just affects two things: my chances of falling asleep and my chances of succeeding in a WILD attempt. A comfy position is always the best… it makes you feel good. So, it doesn’t affect LD’ing ,or it affects it in something like 0,001 way 
During sleep paralyzes your body will come out of it (so also your dreams) when your body senses that there is something wrong. This mechanism makes sure you’re not lying on your arm until it turns purple. So the only main thing to keep in mind for (lucid) dreaming is that you must make sure you’re not restricting breathing or blood supply of any body parts.
the reason why most books want you to sleep on your back is because sleep paralysis sets in quicker when you are on your back. that being said, sleeping on your back would be more helpful if you are attempting WILDs. as for MILDs and DILDs, i dont thinking your position matters at all. personally i prefer trying WILDs on my side because then you dont have the urge to swallow, even if it will take longer for SP to set in.
I totally agree with you both ! But sleeping position itself doesn’t affect LD’ing - only methods and a good sleep.