Should I stay friends with this girl?

She seems a little weird and confused to me. And you should just kind of ignore her (dont be too nice!) just so she gets the idea that you arent ready to be good friends again, and maybe never will be? If she takes it to the extreme just explain to her how many times you caaught her in a llie and you dont like being around liers, it just leads to more problems. I think thats the best you can do for now, goodluckk.