Agree with above advice.
She is supposed to be seeing a psychiatrist, but is she, and is she telling the truth there? Is she taking the meds right? Thats really her responsibility, but maybe, MAYBE thats it. Its hard to walk in someone else's shoes.
Suicide should never be taken lightly. She should have been instructed as to what to do if she feels this happening. You can't imagine how terrifying these thoughts are. She needs someone to stay or be with her, make sure dangerous things like pills and things she could hurt herself on are not right there, and could be impulsively picked up. The ER is the best place for her.
As far as one day being suicidal, then the next day on top of the world, that is the nature of Bipolar. Mood swings. She may not be faking at all.
The lying is getting on your nerves, along with the drama. It would anybody. Deep down, I think you care. With further evaluation and treatment she will return to a nicer person.