I think telling the truth could be beneficial for you in the long run. Ts are used to clients telling some lies- I did, I denied stg happened in the beginning, after 3yr I came clean. It was awkward, however, my T was pretty great about that- said he shouldn't have asked in the first place, we did talk about why I felt I couldn't tell him though. So be prepared for that to happen.
I do lie quite a lot , to my friends and family I keep pretending I have a BF (8yr now, on and off thing, his name, pic, job... everything and sometimes it does feel real:/) Pathetic I know and it's difficult, incredibly time-consuming and I do wish I didn't have to but than try to explain that I've never been in RS (BF/GF), am not looking for one, not go into CSA stuff and still keep the facade of being (quite) normal- can't happen:/
So for me having the one person(=T) I can be 100% honest with is therapeutical in it's self.