This is one of the con's of the internet. She could be doing this due to a mental condition or underlying need. She could be doing it to troll because she's bored. She could have an ulterior motive.

And that's the other thing-you will never know the reason either, unless she confesses and shows proof of her true identity, ie Facebook. By continuing to be her friend and ignoring the lies, you are encouraging a behavior that is not acceptable and could potentially hurt a lot of people.

Give her an ultimatem...she either starts telling the truth or you're done.