What causes lower right pain in the stomach?

See a doctor. When you say "stomach" I assume you mean your abdomen. There are many things that can cause pain in that region, but the classic concern for right lower abdominal pain is appendicitis. If you are having such a pain, go to the emergency room.
Multiple causes. This location could be related to muscular pain and moving deeper the appendix, the right colon, the kidney and possibly referred back pain. If this pain is severe or persistent see your local physician to try to uncover the cause of the pain.