I had no idea who LP was so went to Google and spotted her Wiki. Interestingly, she too has PTSD (although hers is CPTSD) - did Jack claim to have this before she met this woman?
Or was it never mentioned until afterwards? #genuinequestion
They do look somewhat alike, although LP is slightly "better looking" (IMHO), so I can understand them being mistaken for one another ~from a distance~
LP is a "proper" writer though, with award nominations and stuff - something that could make a not-so-successful and definitely NOT THAT FAMOUS writer jealous. That's the extent of my knowledge and I'll stop there, or I'll end up down another twatter-style rabbit hole!
Jack is a bit like Hunch: they both think they're so famous that everyone knows them, yet nobody outside their niches has even heard of them.