I had this problem too, a
lthough mine is an iPod Video (also known as a 5th gen). They started out as one horizontal line on the right side of the screen, then started going diagonal and vertical, and then another horizontal line... I ordered a new LCD screen on eBay($15?) and just put it in. The lines are gone!!! If you can't change the screen yourself, any iPhone repair place should be able to do it.
