Why are mains mains of anybody? Because they enjoy the champ, strength of the champ doesn't factor in.
If your question is why is Lee played a lot when he is claimed to be weak, that can be answered in a couple ways.
He's not necessarily weak. That's evident by his powerful early game, however, he falls off far harder than any champ I can think of, and his best chance of winning late game is giving kills to the carries, which can be difficult considering his strength in the early game and likeliness of taking kills. The last nerf on his ultimate only made his late game worse and barely affecting him early Game, making him far more reliant during that time.
Lee also has a very satisfying playstyle, much like riven, yasuo and draven. Playing correctly and executing their skills precisely give the player a higher sense of accomplishment. Their skills also meld together very well, allowing complex mechanics to shine.