This is the first time that I've ever spent any time watching someone play video games. It seems like an odd concept, but I find it very interesting to compare my reactions with someone else's as they play through a fantastic game.
My Lee was sweet on Carly as well and losing her was as devastated as I've ever been while playing a video game. I was caught even more off guard than you were because I didn't see Lily reaching for the gun.
Anyway, you missed a few nice moments at the hotel with Carly. After you go around and tell everyone about your past, if you go back up and talk to Carly again, it's very obvious there is a romance brewing. Also, while you are walking around doing your investigation, there is an option to just look up at Carly. When you do, it shows a close up of her face and she's giving you the googly eyes.
Maybe it's good you missed those parts, as it would have been that much more difficult for you to cope with Carly's death.
I fucking love this game...