There are a few scenes that indicate he did, the most noticeable been how cut up about it he seems when the Gargain was destroyed. Had he learned to like Starfleet or was it purely just "humanity first" pride?
Did he like Starfleet? I doubt it. I believe he was proud of the work he'd done on the Disco crew, turning them from "polite scientists" into a battle hardened crew. Indeed, I suspect his reaction to the destruction of the Gagarin was more an act to make the crew feel bad for their failure and motivate them to fight harder in the next battle. Indeed, he even said he would have gladly have offered any of the Disco crew to join him if he didn't know for a fact they were "brainwashed to worship the Federation." So, in the end, he still felt Starfleet/the Federation could fuck off, but there was room in his heart for his crew.
Yeah, this. On my most recent rewatch, I actually went into that episode forgetting whether or not he said anything remotely kind concerning his crew after the reveal. I’m glad he did. It helps sell the turn — because while Burnham was the predominant target of his affections, he really doesn’t seem in love with the idea of killing the rest of them, either.
I don't think Lorca truly held any ill will against Starfleet (or anyone else) of the prime universe. All he wanted was to get home. While he was stuck in the prime 'verse, I do believe he did everything he could to help the Federation win the war against the Klingons.
Only as a matter of self-preservation. He knew that if the Klingons defeated the Federation he was screwed and so were his chances of returning to the Mirror Universe. If he did give any kind of a damn about the Federation beyond a means of his own self-preservation, he'd have tried to find a means of sending them the intel they needed to detect cloaked Klingon ships rather than instant head back to the MU the minute he could without a second though as the the much needed intel that could turn the tide in the war.
He worked with the Federation so long as there was a mutual interest and he would benefit. Once his goals were achieved it didn't matter.
I like to think that he came to respect their ingenuity and found some like the chief of security to be not dissimilar to people from the MU so could see the similarities. The MU were not 'heartless' as such. They certainly showed evidence of PU emotion and attachments and I think Lorca felt a strong connection to anyone else who was on the front line with him so probably genuinely was saddened by the loss of the Gagarin - likely though that the feelings were for a different reason than the PU crew felt.
If @The Wormhole is suggesting that Lorca would have abandoned the Federation as soon as he found a way back home - I'm not really seeing that. He's not that cold-blooded. (MU Georgiou might have behaved that way, but Lorca, IMHO, would not.) Besides, it's unlikely he would have been able to find such a shortcut anyway. Realistically, Discovery would not have been able to get him home until the war was over. So, yes, it is in his self-interest to help the Federation win the war, but I believe he did everything he could to that end. I mean, it's not like he likes the Klingons any better than they do, right? Also: What @Ianburns252 said. On that I think we can all agree. Whatever Lorca's attitude towards the Federation may have been - it's still his crew, parallel universes be damned. He'll stick up for his own crew, no matter where they're from.
Lorca was a man of both principle and practicality. He didn't like to loose, and he wanted to stack the odds in his familiar. So, he and the Federation had a "mutual interest" for a while.
But that's literally what he did. In the midseason finale in season 1 he had figured out a way back to the MU and he immediately went ahead and went, screwing the Federation over in the process. He didn't share the intel Disco obtained about detecting cloaked Klingon ships. The Federation went without that until after Disco returned from the MU.
I don't think he liked Starfleet. If you think he liked it, congratulations. You were fooled. He might've come to like his crew, but he never liked Starfleet itself. He chaffed against Starfleet the entire time he was posing as the "real" Captain Lorca. He loved blowing them off. Yeah, he was proud he was able to mold the Discovery crew to some extent. But he only ever saw them as a means to an end. The ship had the Spore Drive, he could use it to get back home, and once his need for Discovery was over, that was it.
If Emperor Georgiou could find secret value in the Federation to want to risk her life to change the MU, Lorca could eventually be turned as well, I think. I would, however, like to see Prime Lorca to see just how different (or alike) he was from his counterpart. Now that we’re in the 32nd century, however, I doubt we’ll have an opportunity to see that happen. He likely doesn’t have the benefit of a Red Angel Suit. He might possibly make an appearance in SNW, though. I’d like to see that, I think...
I don't think Lorca ever really drank the root beer. But he may have eventually if he, y'know...hadn't been vaporized.