Your granddaughter will not be helped with what is troubling her by demanding that she stop all lying and stealing or you'll throw her out. As much as you think this ultimatum might scare her into behaving properly, I'm betting it won't. It'll just show you don't love her unconditionally, which she probably feels anyway and it will push her into having to one-up you with her response.
I strongly suggest that you say something like, "I obviously don't understand what's causing you so much hurt inside. I know you don't feel good about stealing and lying and I want to help you feel better. I'm going to make some calls and find out the names of a few therapists who you could trust and you can interview them to see which one you want to work with. I'll support you in any way I can so that you can feel better about yourself. I know it's tough being a teenager these days but I can't sit by and see you do things that show such disrespect for yourself. Our deal is that I'll try to get you the help you need if you promise to work hard to help yourself. I know you can do it!"
Forgive her grandmother and become her champion if she'll let you. Good luck.