I don't know if it affects nightmares, but I have heard that sleeping on your back is more likely to cause sleep paralysis, so I suppose it could affect nightmares too.

A lot of people first develop lucidity to deal with nightmares, I think some of my first lucid dreams were nightmares, and I've even heard stories of people who naturally lucid dream all the time after developing lucidity to defeat recurring nightmares, so you probably could use nightmares to increase your ability to lucid dream, although I wouldn't use it as a primary method of becoming lucid.