Obviously Lee isnt going to die, that would be the unexpected turn. That maybe somehow he is immune.
Anyone ever heard about a zombie universe where someone isnt immune?, there is always someone immune

and ill bet you that my main man Lee here is.
Also its kinda odd, if you got bid in your arm like that, the smart thing would be instantly to take your belt off strap around you arm stop blood flow to stop contamination and then proceed to cut off the arm, thus you survive.
Just because you get bid, you arent instantly dead, the blood doesnt circulate that fast in our bodies.
Sure it sucks to loose and arm, but better loosing an arm than being dead.