How would you feel about this?

My boyfriend and I had a conversation last night about boundaries that brought up a lot of things. (This is a new relationship.) I specifically asked him about one woman bc their history stood out to me. I asked if I should expect that they will keep in touch and have conversations. He said he’d never reach out to her just to start a conversation, but would respond if she did. Long story short, I found out later that night that he had actually reached out to her the day before. (To tell her about a dream he had about her. Possibly harmless, but it was the fact he straight lied when he had the opp to be honest when I asked.) Also found out that night he went to the strip club the previous night, which he hid from me. (We had already discussed that topic and he knew I wasn’t comfortable with it.) Now today, he has been discussing this whole ordeal with the same girl and telling her what’s going on between us.