My boyfriend lied to me and I don’t know what to do.... should I leave or stay?

He lied about who the person was that he was communicating with. And the person he was communicating with they had a thing for each other in the past. The communication wasn’t flirting from what I seen but it makes me think why does she feel so comfortable to reach out to you and do you talk to her more than what I’ve seen and why would he lie about who she was