Wow. I see some of us are stuck in the stages of dealing with grief and loss.
Stage 1: Denial
In the Walking Dead universe, if you are bitten you die. The bite is 100% fatal and always leads to death, unless immediate amputation occurs.
Lee took too long to cut his arm off (if he does it at all). By the time he decides (or doesn't decide) to cut it off, he has already passed out once. This means the infection is already affecting him; it has spread too far to be stopped.
Even if Clementine missed (if she was told to shoot him), and given how good a shot she is now, I find that highly impossible, Lee is still infected. He can't survive a bite.
Even if Kenny or some magical rescue team arrived on the scene, there is nothing that can be done for Lee. This game follows comic book canon, and as Kirkman himself as said, there is no cure, there is nothing that can prevent a zombie bite from killing someone except for immediate amputation. And that didn't happen.
Face it. Lee is dead.
Enjoy stages 2-5.
Anger: "WHY TELLTALE DID YOU HAVE TO KILL LEE I HATE YOU I WILL NEVER BUY ANOTHER GAME FROM YOU YOU ARE MONSTERS GARBLE GARBLE RAGE RAGE DEATH THREATS" etc.
Bargaining: "Please Telltale, I'll buy every game you've ever made if you just let Lee live into season 2. I'll do anything. Please."
Depression and Acceptance: Most of us are here, waiting for you to catch up.
Lee is gone.