Cornwell went over to speak in Sarek's place. Before she left, she wanted to have Lorca relieved from his command because he's lost it. When Cornwell is captured by the Klingons, he should've rescued her. He's not one to care about rules and regulations and everyone expects this pattern of behavior from him anyway. So, then, at that time, he suddenly decides to play Mr. Squeaky Clean I Do It By The Book.
I'm personally calling Bullshit. If he doesn't rescue her, he gets to keep his command because Cornwell won't be around to take Discovery away from him afterwards. She was going to do that anyway, regardless of what happened, if she survived.
I think Lorca, no matter how much he has a thing for Cornwell, loves Discovery, loves being in command of it, loves that he has the Spore Drive, and loves that he's finally getting to kick all kinds of ass in this war. He's that type of guy. He loves this. That trophy room of his isn't just for show. Taking it all away from him would hurt him worse than anything else, so he's in Preservation Mode. By not rescuing Cornwell, he's letting her die.
Even Saru questions it and points out that normally Lorca would go in guns-a-blazin' charging to the rescue. Yeah, he might've had a "wake up moment", it's possible, but it probably comes down to you guys think he's a better person than I do. I don't necessarily think he's a villain but I also think he's more-than-a-little crooked and I think he's amoral.
Same with the "one more jump" in the mid-season finale with Stamets. This is a guy who saved his own skin in his previous command and no one else's while they went down with the ship. If you put Lorca in Sisko's place in "In the Pale Moonlight", I don't think he'd blink an eye. He wouldn't go through any of the anguish Sisko did, and that's what makes him so different.
So, that's where I'm coming from and why I think Lorca was willing to let Cornwell die by not rescuing her. He was looking out for Number One, and I don't mean Michael Burnham.