She was a foster child? She might have learned very early that exaggerating got her the attention she craved and needed. Did that occur to you?
It sounds less like she is lying than like she is exaggerating about a lot of little, day-to-day things; she isn't accusing people of dire crimes, is she? If she's mostly exaggerating about a lot of dumb, as you say "random," things, she sounds as if she has some mental and/or emotional issues and always has.
While your frustration with it is understandable, have you ever tried talking to her about therapy, as several other folks on here have suggested? She likely has NO idea that she is doing this; it's so ingrained after so long that it's unconsciously done, and she probably would be utterly shocked if you said, "You are lying about X" because she doesn't see it at all. I'm not saying that to let her off the hook, but I am saying she seems to do this as naturally as she breathes, so it sounds like a coping mechanism she developed long before you came along....so don't consider it a person affront to you, but a serious mental issue for her.
Can you manage to see it that way and either live with it and find some other good in her, or try to help her? Because I don't see any affection for any other part of her in your post. If you feel anything for her, I'd try to get her some help somehow, OR learn to focus solely on the parts of her you like and not engage with her any attempts to convince her that anything she says is wrong. Not a fun way to have a relationship, but short of her getting serious mental help, or you breaking off all relations with her, what else can you do?