Can Lazy Eye Affect Sleep?

I am 52 years old and have a lazy eye. I have a dead spot in my right eye (not completely formed) which causes weakness of vision up close and weaker than normal vision even with glasses. I had the eye surgically repaired to keep it from floating outward to the lid and now it stays pretty normal until late at night. It now will move toward the inside (toward nose) but doesn't move nearly as much as before the surgical procedure was done. My question is can a lazy eye effect your sleep at night. I notice that when I close my eyes at night the lazy eye seems less controllable and I am wondering if that effects REM sleep. I wake up tired all the time and it is usually after a 7 to 8 hours of sleep. Please Advise !! Thanks