Oh no! I am so sorry your friend does this to you. I think we have all had a friend like this or been a friend like this to someone before. Usually if a girl is acting this way it means she is really worried that if she shares you with someone else, you will not be there for her. It can be a tough situation. I think you need to be honest with your friend and tell her how you feel, that you will still be her friend and that sometimes you need to do other things at lunch and with other people. Re assure her that you are still her friend even when you are not sitting right beside her.
Hopefully your friend will understand.