If I kill Savage Lee and get Unkempt Harold, am I able to get that gun again at a later level by grinding him again, or will it only drop once?
Savage Lee will spawn every time you load up Three Horns Divide (after you complete and turn in the quest The Road to Sanctuary).
This occurs whether or not he previously dropped an Unkempt Harold, so you can farm him as much as you'd like. This is commonly how players get Harolds with desirable parts such as the double-penetrating prefix and the Torgue grip.
Legendaries in general will drop by the cartload, if you replay the locations or quests where they have an increased drop rate. Sometimes they'll drop more often than you expect, and they'll drop so often that you're selling them off. This is how people deliberately acquire Bees, Norfleets, and other highly popular oranges. And how I acquire massive numbers of unpopular oranges, such as Skullmashers or Whiskey Tango Foxtrots. :-P