What to do about a friend who keeps lying and starting drama? Please help?

After I stop hanging out with my former best friend because of all the drama she was creating and all the lies she told, I moved lunch tables to sit with Lexi. We grew a lot closer and I thought it would be great since she seemed so drama free. But after I became really close with Sadie who has been friends with Lexi for a while everything changed. Lexi gets jealous whenever Sadie and I hang out and seems to want me all to herself. If I make plans to hang out with Sadie alone Lexi flips out and starts a fight and cries b.c she wants to all hang out as a group and we always wind up feeling bad and I invite her to come along. But Lexi always wants to hang out with me alone and doesn't care if the situations reversed and Sadie wants to hang out all three of us. She always talks about Sadie behind her back saying lies trying to make her seem dirty and gross and stupid, etc. She always makes fun of Sadies weight behind her back. And she always lies about her family life and problems she has to make me sympathetic towards her so I'll take her side but I'm trying so hard to remain neutral. Even if me and Sadie make plans to go to the movies and we invite Lexi, if Lexi isn't allowed to go she gets angry at US and cries about it. I just don't know what to do because I can't handle the drama but I don't wanna drop Lexi as a friend either. So last night we were all fighting because last week I made plans with Sadie for this coming weekend. Sadie was upset that Lexi always comes in the way of us hanging out so we agreed that this will be the one time we hang out without letting Lexi interfere with it and ruin our plans by making drama. Later the same day Lexi asked if I could sleepover that night and I said I probably could because I thought me and Sadie would be done hanging out by then, but after I said I probably could Lexi told Sadie and Sadie got upset because she wanted to hang out till late at night and Lexi wanted to come at 4. I told Lexi I was sorry and we could reschedule or I could just come at around 11 at night. Lexi started a huge fight and was crying all night and texting me mean things and lies about how terrible her life is (I know she has problems because we all do but her life really isn't so bad, her family all loves her very much and shes spoiled rotten). Sadie got so upset that she cut herself (not bad, onyl with her nail and she swore to me she'd never do it again). Lexi found out and knew i was sympathetic towards Sadie because of that so today she told me things that I know are lies about her taking pills for clinical depression and then she took a picture of an old cut on her leg and tried to pass it off as her slitting her wrists. Who should I hang out with Saturday? How can I stop Lexi from feeling so jealous all the time and from thinking that she has to earn my sympathy? How can I stop there terrible rivalry I'm getting caught in between? Please please please help me.