The first thing you should ask yourself is why is the girl lying and saying she has a boyfriend if you know she does not? It could be that she wants to play games and in which case your whole future relationship could then in fact become a childish game to her. You will spend the relationship caught up in stupid games and drama. The other reason she may say she has a boyfriend is because she might be scared of liking you. I would say talk to her and ask her why she is lying about having a boyfriend. If she denies lying and you know she is lying then move on.
The situation just sounds very young and unexperienced. She is probably very shy and trying to impress you at the same time. She wants you to think that shes done the relationship thing before. If you care for her, ask her about it gently...she will probably come clean if she knows she won't be judged.