I completely understand you and have been in a similar situation. Sometimes I feel as if I'm being eaten alive by guilt.
I get the feeling of "let it go, never bring it up again and it will go away".
Though you should be 100% honest with your T for the relationship and therapy to be beneficial, I have made the personal decision to not tell her the truth. I, for sure, will not do it again. I just have such an amazing relationship and bond with her that it would devastate me to lose her trust and potentially have her terminate me as a client. She told me if the time ever comes where she takes something I say or do personally, she will have no choice but to terminate for ethical reasons and refer me to a new T. The reason for this is that she would have a warped perception of me and that would really get in the way of being able to help me, moving forward.
I do feel as if I need to "come clean" about the lie though. Even though I am already pretty sure of my reason for lying, I do feel it needs to be further explored. I decided to do this with a new therapist, though. Someone who is unbiased and could look at the situation objectively.
I know it's a crummy feeling.