We don't know that's what happened, though. She's an admiral, he's a captain. He didn't order her to go. She was the logical choice to step up in Sarek's steed. What he did after she was captured is another matter entirely, but even then, it's obvious that he was conflicted and torn. I get no impression that Lorca is purposely putting people in danger because he's an asshole. Indeed, the opening of this episode shows what kind of a man Lorca is. Trying to put his ship in the line of fire to save others demonstrates his character.
I think Lorca calculated the odds and realized there was a good chance Katrina would be captured, but also realized he might lose the game of chance himself. His “sin” was his failure to disobey the rules and try to rescue her, as he likely would have done otherwise, because of what she knows and her decision to remove him from the captaincy. Katrina knows him well and has reason to be angry on a personal level, if not on a professional one.