Empty ultimatums are definitely a bad idea.
She is however, lying about the little things which tell me that she's definitely going to lie about the big things.
You both need to try to find a way to understand why she's lying - is she afraid of conflict? is she trying to avoid the issue? Is she a compulsive liar? Is she afraid of your reaction - do you tend to get angry over the little things? Did she have abusive parents? It could be one of a million things...
In the end it comes down to the fact that for some reason or other, she's not comfortable telling the truth. I would recommend working with a counselor to help her, and you, get to the bottom of the underlying issue.
I would not threaten to end the relationship, unless you mean it. If you say to her;
One more lie and I'm leaving..." Then you better be prepared to leave and be without her.
Don't make empty threats to try to control her. If this is serious enough for you to leave, then leave - don't make threats... That's your attempt to feel in control when in fact you cannot really control her actions. What you can do is tell her how you feel when she lies to you rather than blaming and criticizing. Tell her: I feel hurt, angry, sad, insecure about our relationship, etc. Put it in terms of your feelings.