Also worth remembering that there were more than a few Starfleet officers in canon, in STVI, who were dead-set against trusting the Klingons, including Admiral Cartwright, who seemed to be respected, and Lt. Valeris, Spock’s hand-picked protege. Your Lorca would probably have at least a few others on his side.
In redesign AU, a lot of humans and other species would be very very scared of Klingons. A lot of Klingons would view humans like we view say mice. A small mammal, that is just around. Mostly you don’t bother with them. Some people will kill mice and consider them pests, some people will keep mice as pets. But basically nobody is going to say that mouse stands as an equal to them. Even the nicest Klingon will do little more than nudge humans out of their way. That kind of attitude isn’t actually one well-suited to good equal relations between species.
Even if people aren’t mistrustful of them because there’s been a direct Klingon-Federation war (there has not), they would still get a bad feeling from the way most Klingons would treat them and speak of them. Not to mention of course that the group of Klingon who agree with attacking the Federation didn’t give the best impression to start with, and it wasn’t drastically improved when other Klingon intervened purely because they found the act insulting rather than because they wanted anything to do with Federation lives. Federation lives are saved simply because some Klingon feel killing them would be degrading to Klingons. That’s patronising as anything lmao.
So Lorca has a lot of ammunition, honestly. A few choice words here and there, and he’ll easily be able to play on fears about Klingons.