The basic idea when you are laning against Akali as lee sin is to use E to negate her W and lifesteal away your harass... once you manage to grab a few items you can fight a war of attrition that ends when you either get a hexdrinker at which point you can engage her with impunity. However, if she manages to get a hextech she can beat you at sustain, and the lane will get significantly harder, though not impossible.
Akali's main strengths in lane are her sustain, invisibility, and hard engages. You can keep up with her sustain and her Invisibility is directly countered, so it basically comes up to "whoever punches who harder". As someone who has played this match multiple times, I can say this: Lee punches harder.
But many lee players play this matchup and ask "WTF? How am I losing? Doesn't lee harder counter akali?". Yes, he does, but just because Lee punches harder doesn't mean that Akali punches any less hard. She still has one of the highest bursts in the game. This is why hexdrinker is an important part of this matchup: It ensure that, baring ganks, you cannot be completely bursted down unless she is fed.
Since a good, knowledgeable akali can circumvent this "counter" with enough experience, it's skill based, but lee sin is still one of the best counters to akali around.
