Alas, I guess I didn't read your post correctly. My bad.
Then you have to have good mobility, and be able to handle yourself early. However, if you run anyone that has a stronger late game, you'll do far more late. Or I suppose if you can out burst him, and then sustain between his pokes. I guess Olaf might be a good pick. Throw an E on him whenever he tries to kick you.
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IMO i think anyone who can out sustain him.
His W(i think that its his W) gives him relatively good sustain.
So if you can outsustain his pokes while still poking him you should be good.
Two champs that come to mind are Vlad and Olaf
Vlads Q gives him good sustain
While olaf's w gives him his own lifesteal and his q will slow Lee sin down