Is a borderline friend worth keeping?

Don't leave her. to be honest it seems like she could really use your friendship right now. maybe you really mean something to her but she cant tell you. and if shes lying all the time that could just be a cry for help. even with all those friends its possible for someone to feel completely alone. if she has BPD it might be hard to tell. but you should be there for her. as for telling your sister, its up to you depending on how you think she will react to this.