Considering how "well" she does her primary job--psychiatry--that isn't saying much. I can chalk it up to bad writing (though, for god's sake, writers do have access to search engines and they can look up the symptoms of PTSD vs Acute Stress Disorder and figure out the difference...) but, since she's shown to be ethically conflicted in the first place--sleeping with your patient? Really...---not so sure we're not looking at a clever attempt by the writers at misdirection. And, yes, the same writers who craft schlocky psychiatry/psychology can, nonetheless, be clever at making us think they're implying Lorca is MU.
Still, I'm a big Lorca Apologist, so...I'd like to think he's Prime Universe's Lorca but, hell, I'd be satisfied with MU Lorca so long as they keep him around.
Starfleet, historically, don’t really get PTSD. At least...very rarely. Grows out of that old astronaut best of the best mentality of early SF. It’s also because there would be nothing but PTSD stories by about three episodes in. Exhibit A: O’Brien. A man fucked with, fucked up, and just generally fucked so often, that by at least season three of Ds9 his closest relationship really should be with Bashir, because he would be on meds and in long term treatment. But he’s unlucky even by Starfleet standards. This is a job with death, more death, a side of abduction, possession, injury and the occasional time slip or meeting of yourself. It almost makes Genes viewpoint on Jeremy Aster in TNG understandable. These people undergo stresses that humans now never have, and joke about it at the coffee machine. I mean ok, Kirk never had a window, but everyone else sleeps literally about a foot away from the most hostile environment short of swimming in lava that the universe has to offer. PTSD in Star Treks narrative basically makes no sense. From a certain point of view. It only comes up when we are doing Vietnam in Space Basically. (Ds9 here and there, Picard with the Borg. Never, oddly, post Gul Madred or Sarek or...I forget his Ressikian name.) I also don’t think he’s Cornwells patient. Subordinate, possibly, friend yes...but she’s not treating him.
It’s telling that most of the time we see Troi doing her job, it’s for run of the mill stuff mostly. (Relationships, personality issues, family issues) and rarely the seriously messed up stuff that happens in Starfleet.
It’s something that’s inconsistent in DSC too...Lorca has PTSD? What about the Shenzou crew? The prisoners who watch their pilot killed? Burnham herself?
The Disco is the ship of the Damaged, but none of them really are...except when we need them to be. Even Ash, and what he thinks he remembers (way to backtrack on your Male rape survivor story DSC team..though we can see why you did.) is basically what O’Brien would call ‘Tuesday’ not that far in the future.
It’s a tricky place for Trek to go to, and has only really sort of panned out once or twice in the past (Siskos wife, Nogs leg, Picard and the Borg Queen. Though that may have broken the Picard character for the remaining films.) and Lorca trip to the agoniser booths here will by necessity just be another day ending in y.