Making sense of a TV show and it's characters can sometimes be an incredibly complicated task particularly with a series that is using the format of Discovery. We aren't given all the answers at the end of the episode hence people are going to make their own assumptions and opinions based on any number of factors until proven otherwise. It's understandable that many people will take issue with some of the actions the characters make in Discovery, especially in light of what we see in other Star Trek series.
Maybe the point of the story at the moment is that we are not supposed to like this starfleet. The Starfleet we are seeing is one that we haven't really seen before. As far as we know, Starfleet hasn't been in a conflict with another power since the Romulan War. They are clearly unprepared for a war with the Klingons, and the Federation is apparently losing the war. They are getting desperate and starting to make desperate decisions. The way starfleet is acting is similar to how some real world powers have reacted to similar scenarios. I'm not saying that these decisions are right, but it makes them understandable. I think this whole story arc will be about how a civilisations morals and ethics and values survive threats to its existence. For me that means, seeing people fall and then being given the opportunity to make the right choices and better themselves. Captain Georgiou is representative of the Starfleet values we all hold dear, Lorca is the polar opposite of that. There is a purpose for this beyond it being edgy and cool, to have a jerk captain. Sarek says in the second episode that Georgiou was someone who had lost everything and maintained hope, I think Lorca is the other side. He's someone who has lost everything and lost hope as well.
We don't know exactly what happened on Lorca's last command. I think the way that he speaks about the incident has some hints as to how it played out and that hsi survival was probably not his choice. The way that Lorca says 'Not my Crew, Not on my watch' when talking about trying to prevent them from being captured suggest that he felt a great deal of responsibility for those under his command. Nothing about Lorca's behaviour suggests to me that he is a coward or would value his own life above that of his crew. He knew how Klingon's tortured their captives but showed zero fear when actually faced with it himself. He didn't buckle under the pressure of the situation but formulated a plan to escape and whilst he left mudd behind, he made sure to take a starfleet officer who may or may not be a Klingon spy, even though Lorca suspected this himself. I get the impression that Lorca is dealing with survivor's guilt and this may be influencing his decision making. I agree with you that Lorca is a damaged man and I think he compartmentalises it hides behind a cold seemingly callous exterior.
We've never seen this level of moral ambiguity or complication in main characters in a star trek series before. It takes a lot of getting used to, but i feel like at the end of this season we'll be able to look back and hopefully say, 'this was star trek'
