OK, here is my perspective as a Christian. Difficult situation for sure. This is based on my experiences with similar situations and wise counsel from friends and pastors. Seeking counsel is a wise thing to do, and lots of prayer helps too.
I think you need to ask her about it in a way that is not accusatory and gives her the benefit of the doubt such as "Someone told me you were taking credit for writing the song my team wrote. Can you explain why someone would say something like that?" Then base your response to how she answers. Try to be logical and keep emotions out of it so that she does not become upset or defensive.
Hopefully, she will realize she was wrong and apologize. If not, you can warn her of the harm her lies could cause both of you. The fact that someone has already caught her in a lie has harmed her credibility as a performer, and could embarrass her and destroy her reputation. She seems to be seeking attention for herself and people's adulation, and you know that does not work.
Lies also tend to spin in a way that hurts everyone involved If they are not dealt with. Before you know it, someone could accuse you of lying when you give yourself credit for your own song! Our reputations in the community are fragile things - that is why one of the commandments is not to "bear false witness" against a neighbor. Our reputations are a big deal.
After talking to her, you can feel assured you have done what you could to resolve the situation and have taken steps to forgiving her. Then you can leave it in God's hands. If she continues to lie, she is going to shoot herself in the foot in any case.
Congrats on a successful comedy career, by the way.