He turned to a walker (well, almost), though, Clementine put Lee to rest because it was the right thing to do.
Supposedly chopping off of the arm should also remove the infection, but it spread by that time which made it pointless to saw his arm off.
Episode 5 kind of felt pretty fast compared to the others which lasted longer, but I'll be sure to replay it again. ;)
Note: I thought chopping off the arm would solve Lee's problem because the TV series proved that the infection would stop if the arm/leg were taken apart.