I agree that you should definitely try to help this girl feel more secure, but at the same time cannot let the lying go unpunished. She will rebel against the punishment now, but may thank you when she's an adult.
My youngest daughter began lying just before she began high school. All my kids always knew that honesty was the most important thing in our house. Tell the truth when you did something you shouldn't --- you'll certainly be punished, but lie and the punishment will be twice as bad. Looking back, and reading the other responses, I realize she was insecure and doubting herself and this was the manifestation. She was grounded more often than not during her high school years, but to this day will lie if she feels like she's in a tight spot.
She always has a big, complicated story about why she didn't do something or why her paycheck is late or why she's late, and on and on. There's always drama in her life, all of which she creates. We listen to her tall tales but even when they sound sensible and possible, we can't really believe her because she lies about so many things.
She has talked to me a couple of times about being upset because she knows we don't trust her or believe her, but she continues to lie. There's a disconnect in her somewhere about the connection between lying and trust. And even though she KNOWS we don't believe her, she'll tell her entire big story every time.
I love her with all my heart, but truthfully am not that connected to anything that happens in her life because I can't tell anymore what's true and what's not, so I've kind of stopped caring in that way. We talk about other things, go shopping and hang out, but there's not a real connection because of the trust issue.
She has a new set of friends every 6 months or so --- she'll tell you a wild tale about why they're not friends anymore, but I think it's because they also get tired of the lies and drift away.
It makes me sad to see her without any real long-lasting relationships, but I'm hoping she realizes someday how important being honest is.
Good luck and stay with it! She'll be a better person for your involvement!