I'm so sorry you are dealing with such dirtbag behavior.
I don't know what state you are in, but in my state it is actually illegal to share pornographic images with a minor. I would have a discussion with your lawyer. Every state is different.
You mentioned in your last line that you are "so thankful to be separated from his bad decisions".
I'm in the same boat. My XH flirts with anything that moves and my sons are grossed out by it. He is secretive, so he didn't share with anyone about his AP/OW - but they all know now. My sons are older than yours, but my youngest is still going through it and hasn't been able to separate himself emotionally from his dad's stuff.
I listen and validate and remind him that he has agency. He is free to speak to his dad about things that upset him. (We all know it doesn't do any good to change the behavior, but I encourage the boys to communicate and control what they can - themselves). At his age, he is free to have no contact, or contact with boundaries, which he is getting better at. I HIGHLY recommend the book "Boundaries" for everyone. There is also a "Boundaries for Teens". At any rate, your S15 could read about boundaries from reputable sources if he doesn't want to see a therapist.
I just wonder with your sons ages if they even have to have any relationship with their dad right now, while the behaviors are so gross. I encouraged my sons to speak to other adult men about it. Kept me from projecting, and gave them an unbiased male figure to hear them.
Maybe talk to the L and let the L explain to the boys what they have to do, given their ages, so that you aren't held in contempt, but they have choices on what they are exposed to. For instance, if they don't want to see their dad, they should at that age be able to choose, or maybe it can be limited due to his mental instability.
I wish you all the best. You aren't alone (((hugs)))
ME47 XH44, S28 S24 S19
8/17-BD IHS: 1/17-2/19 D FILED (ME): 7/19 D FINAL: 10/20 M23 T25 OW CONFIRMED: 01/21
Do not let your hearts be troubled and do not be afraid.