Wow, I'm sorry. Vipers in your pit are the worst vipers. The worst example of me getting bitch slapped by a "friend" was not without precedent in her behavior. The first time is happened, I stopped telling her (as much) stuff, seeking out support from her, and I went a long way towards undermining her relationships with mutual friends. Mostly by loudly and repeatedly pointing out her inherent shittiness. Can't say I'm proud of that, can't say that I'm not proud of it either. I look(ed) at it as keeping her away from me and mine for good reason. The moral of this story is still that it hurt. Even with the First time, there was still a Worst time. And for a long time after cutting her off, there was a lot of mental energy invested in chewing the whole thing over. Hell I can still give that one a good raking over. But it is an exhausting proccess. Both to mistrust, and doubt yourself. You say you can't wash your hands of her. I'd very carefully evaluate if this is an isolated incident with any mitigating factors, or whether this is the revelation of a patteren. If it's the former, things should be able to get better. If it's the later I'd try to take some type of break, and put some space between you two. Give yourself some breathing room to look at the incident, your relationship, and to avoid agravating an already icky situation beyond salvation. Ok, I doubt any of that really helps. But I am very sorry. This kind of thing is never ever easy, or pleasent to wade through. I hope it all comes right in the end.

I'm so sorry to hear that such a situation has arisen. Being someone who is very private and doesn't share inner thoughts easily, I can understand what a major thing trust, and broken trust especially, is.
Does not having ulterior motives also mean that you are unaware of any motive for the lying? If the person has no motive for lying it makes things all the more complicated in my opinion. I always find it easier to deal with the things people do if I can understand why they do them. Maybe looking at what is gained by the lying can help in knowing how to handle it.
What to do is a hard question. More than a lot of work, mistrust seems like a large emotional drain. I don't think you should be the one responsible for stopping her lying. It feels like something that only she can really do. But there is the problem of dealing with the person and the mistrust. It sounds like you can't distance yourself from this person, which would be my gut reaction if I were in that position. I'm also going to assume that talking to her about the lying and your loss of trust in her is out as she'd probably deny the behavior and result in making your relationship even more awkward. Though if the other person cares enough to listen, it might be a good thing to do. I guess it all depends on the type of person she is. Will calling her on the lies send her toward denial or toward realization?
In my experience, you almost unconsciously start to quietly doubt the person and proceed to cut yourself, meaning your *real* self, off from them. Not that you don't interact with them, but the content, so to speak, of the interaction is different. Unfortunately in a way, you automatically start devaluing the things they say.
Oh dear, I believe I'm now rambling. Time to stop. Whatever happens, I hope this person doesn't succeed in making you mistrust more. I throughly enjoy the real Quila, and one rotten apple shouldn't get to spoil things for the rest of us. ;)