I like ST: D quite a bit; but that said, there are MANY words I could use to describe Lorca and "Hero" would NOT be one of them - nor do I feel the character is being portrayed as a Hero in any sense.
Star Fleet Command has given him Command of a vessel using wildly unproven and dangerous technology because the war is going very badly for the Federation, and they want to end it ASAP without having to surrender. Captain Gabriel Lorca is:
1) Definitely considered expendable. (Again Starfleet's attempt to get this Spore Drive tech is a 'hail mary'.)
2) His unorthodox actions and decisions are still being tolerated because so far they have yielded gains in the war effort.
And if anything sleeping with an Admiral produced a situation that (if said Admiral survives to report to Command) will lead to loss of his Command and further psychiatric evaluation.
I'd almost call him a hero to those who's lives he's saved, but his actions? don't seem heroic, his motivations don't seem heroic, he seems like an asshole.
I dunno the circumstances surrounding the death of his former crew, but I have a feeling I won't find those heroic either.