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Dude, as Ken said, you're playing them wrong. They're not made for focusing on farming. Yeah, farming is very important, some and most of the times more important than kills, but that's not why they're there.
Your role in that lane is to bully that AP carry, to make his life a living hell in such a way that by the time you're level 9, he'll be two, in the best scenarios three levels behind you, low CS and a morale that can be compared to a mountain of stinking, rotting ****.
Ta-daam! You just won your team the game, because that guy is going to be so pissed and so upset he's gonna spill his frustration on his teammates.
Regarding Fizz specifically, he's got that Dash. Dash, auto, E. Dash, auto, E. It doesn't take more than 1 second, in which that Lux doesn't have time to bind or snare you. She'll be too busy to shield.
It's important to know how to play aggresively in such a way that you won't feed.