This discussion may contain spoilers!
One thing I've been wondering is if you cut off Lee's arm, did he really die because he was too infected or did cutting off the arm really work and the reason he died was due to blood loss. Think about it: Lee doesn't have his blackouts if you cut off his arm which is strange if he really was too infected for it to be effective. If he would have died anyway, he should had blackouts anyway if he was too far gone to be saved by amputation. Furthermore, nobody in the group is a doctor and all that was done to his wound was bandage it. Since amputations need proper care to be dealt with and the wound was still bleeding through, he would have suffered blood loss. Also, another thing I seemed to notice was that Lee looked more like a walker in playthroughs where he kept his arm while he just looked paler if he cut his arm off. Furthermore, in the comics, I think Dale didn't have his leg cut off immediately and he managed to survive. Therefore, I'm in the belief that Lee could have survived if he cut off his arm and he managed to survive through the blood loss.