I told her not to do it, but she did it anyway!
What did you tell her not to do? Did you explain the reason behind it.
I have reason to think that she lied to me, I've asked her to be truthful.
Your request, if reasonable, should have been followed by her. That she didn't shows you that she doesn't respect you.
I can no longer trust her.
You should be upset. That she couldn't be truthful to you, a very reasonable request, shows that she doesn't care about breaking her word to you.