I thought about this. I think it would work best as a passive. He'd have normal vision, but also the ability to sense people in FOW. Just not always.
It would make his Q quite interesting if he could see that there's an enemy on the other side of a wall, but even if his Q hit, he wouldn't be able to tell which enemy that is. Q would no longer reveal, but it'd still travel with the target, and he could still jump to it.
It could also be a passive effect of one of his actives, and go on cooldown along with that ability. To not give him too much early power (he has enough already), it'd make sense to put it on his ulti. First time you level up the ulti, you get this passive. When the ulti is on cooldown, you don't have it anymore.
Another possible way to incorporate it into his kit would be to make it a passive that only works when he's not using his other abilities. This thing would disappear whenever he used an ability, go on a 10-second cooldown or something. 10 seconds is a long time. The idea is that when he's clearing his jungle and securing buffs and stuff, he'd make so much combat noise that he can't hear enemies approach. When he's not fighting or using abilities, he can sense people in the FOW.
The big danger with adding to his already rather loaded kit and giving him too much utility. Since Riot have said that the big thing about Lee is his mobility, and ability to disrupt the enemy team, his E and passive are not necessarily part of that concept. Either or both of them could be remade into something that fits his theme better, and incorporate this special vision thing.