My therapist doesn't help much because she thinks porn is just a fantasy and that I can't ask a man to stop fantasizing about other women.

Well (ignoring her regrettable take on porn for just a second - porn is a damaging fantasy, no question), you can't really police other people's thoughts. The idea that you can or should (in general) can go to scary places. Maybe that was her main point? The fear that a partner is having mere thoughts about other people can overwhelm and debilitate some people. Porn use (especially obsession) is one thing, but there's a difference between that and having a fleeting thought about someone else that you're never going to indulge or act upon.

And yet he lied to me about something he thought was trivial even though to me it induced a panic attack.

He thought it was trivial because pretty much the whole world thinks it's trivial, unfortunately. But it sounds like he's recognizing what you're showing him, and making an effort - do you believe it's sincere?