I think you should not believe her but try as much as you can not to make it show. Let her explain why she thinks she is being honest and after that, you can also tell her why you think she is lying. Maybe to her she is not lying and to you she is lying. That's where the misunderstanding comes in and both of you should talk about it.
Is there proof that she's lying? If there is then bring it to her attention then and there. But make sure because once you accuse someone of something you can't take it back. But don't be afraid to stand up for yourself and put up some boundaries for yourself too, about what is and is not ok for you.