What exactly happens when you lay on your right side? Is it painful or do you have trouble breathing? Im not sure if sleeping on a damaged lung induces hemoptysis, but i seem to have problems with laying on my left side and hemoptysis. Seems my left lung is my bleeder so i try to lay on my right side more. I also do not lay flat to sleep ( induces hemoptysis for me) , i now have a reclining couch and i sleep on that everynight. Maybe you could try sleeping in a more upright position. Not completely upright, but maybe propped up on a stack of pillows so you arent laying flat. Its worht a shot to see if it helps you sleep and not put too much pressure on the right side.