Being an (ex-sorta) league player and Lee being my favorite champion, he isn't skill based at all. Anyone with a brain can figure out how to do all of his cute little plays and his skillset isn't interesting at all except for, like mentioned above, his shield/lifesteal/spellvamp and his AoE reveal.
He's not as difficult to play at an acceptable level as people say, but there's a pretty big gap between a good Lee and a great one.
"Combine Cloak and Dagger with Boots of Swiftness so CC doesn't stop you from moving faster toward defeat." - Frost_shock_FTW
You know, the exact origins and abilities of Lee Sin aside, the core idea behind him--that of a martial artist who uses only gains access to certain abilities after a prior move has been used does seem as though it'd have a bit of potential in DoTA. In a rather rough analogy, this could allow for a hero along the lines of a melee invoker, insofar as he modifies his abilities to match the flow of whatever situation he currently finds himself in. Not that Invokers ability creation system would work well with such a champion mind you, but if I might be so bold as to take a cue from Riot Games, I think they may have been fairly close to the mark with Lee's (Ability 1 > Alt-Ability 1) style. I still don't entirely like this execution as in practice one usually treats both abilities as a single move, thus limiting the range of combos, whereas ideally, I'd like to try and find a way for our hypothetical DotA monk to feel as though there was more of a Street Fighter feel to his abilities, insofar as you could have a great number of different combos available to you, depending on all the factors of the present battle (Ex. Such as how Ryu's Shoryuken makes a great anti-air move, whilst feeling comparatively subpar when used against a grounded target).
While I'm not entirely sold one way or another on how well one could fit such a champion into DotA without having it feel as though it clashed with the style (and gameplay) of the game, I do think that it wouldn't be such a bad idea to consider the potential behind the OP's idea.
"If I have to be at the circus, I want to see the lions and clowns. But no matter where I go the show is always the same. Dead body. Stage left. "