There should be more than a few champs that can beat Lee, I never got that, he does not seem all that amazing to me, but to name a few...
Yorick- should be able to bully and out-sustain him quite easy.
Warwick-Ditto, sustains hard, ult gives guaranteed ganks when jungler shows up. Odd pick yes, but it would work.
Gragas- Should be able to just poke him to death without much effort.
Olaf- Makes his armor from W pointless with his true damage, can build tanky as hell and still do just as much damage as Lee, so should be pretty easy win.
Riven- She does not care about losing AS due to his cripple, so it makes one of his skills pretty much useless, and after that she is basically Lee Sin with shorter range abilities and more damage, play aggressive and should be easy enough win, also once 6 her ult comes into play, which with its very short CD it certainly helps to out trade him.
Xin Zhao- While a tad risky an offensive Xin can shut down lee sin pretty hard, as long as you make sure to only attack at the right times, IE counterattacking after Cripple is down.
Rengar- Sustains is damn impressive, and if maxing W a double W can do more than enough damage for trading as well as of course healing you.
Nidalee- Play passive till 6, then trades should be pretty much in your favor from then on (due to having very spammable skills that is).
Just to name a few, at least in my opinion.