Hi
colleenp 
Although I'm sorry for what has brought you here, I'm glad you found us as we are here for you, to offer support while you navigate your relationship with your DD. We get it, better than anyone else does - we've been in similar situations and we know how difficult things can be.
My DD also lies and it's usually for the same reason your DD stated, she doesn't want me to be disappointed in her. She's also shared that she feels I will judge her. To be fair, I'm guilty of both - being disappointed and judging her. I'm working on eliminating those behaviors, though it's not easy.
It's good you are seeing a T (therapist) and it sounds like s/he's on the mark with validating feelings. Are you in family therapy as well? Is your DD in treatment for BPD in addition to therapy?
I hope to hear more from you,
colleenp, a strong support group can make a difference and that is what we offer here. You are not alone.
~ OH