If Y is believing what X says and is doubting what you say, you'd better have a talk with Y as well as with X.

I notice that you say X spoke about your "alleged conduct", but you didn't exactly say that X was lying. If X wasn't lying, then perhaps Y is feeling as betrayed by you as you are feeling betrayed by X. If this is the case, be prepared to do a lot of work on your friendship with Y.

Whether X was lying or not, it seems that she has already decided to ditch you, whether she's told you outright or not. If she's already expressed this level of disinterest in having a friendship with you, it would be pointless for you to try to "preserve" something that's already spoiled.

My guess is that Y is feeling ambivalent about X as well (Y may be thinking, "Whether or not X is lying to me, she's not being a very good friend to Tiree, so how can I trust her to be a good friend to me?"). You can help convince Y that you can be trusted by resisting the temptation to reveal X's secrets to the world. The important thing here to remember is that it's more important not to damage Y's trust than it is to damage X's reputation (besides, if you tell tales about X, she can just as easily say that you are lying, thereby breeding even more distrust in Y and in others!).