I think there's a difference between lying and changing your mind. Lying is saying something you know to be untrue at the time you said it. Changing your mind could mean you said you would do one thing, having the full intention to do that, but then later something convinced you to do something else instead.

I think your T changed her mind. I think it's very unfortunate that she did, because it seems to have hurt you and your trust for her. I admire you for persevering in working it out with her in spite of that.

I had a former T who told me "I am not going anywhere" and acted very confident that she could help me. Then after a couple months when I was already very attached to her, she referred me to someone else. I felt very hurt/confused/betrayed by the whole thing, and it took me many months to make peace with the fact that she really just didn't know exactly what she was doing with me, in spite of good intentions.