Laning against zed in a nutshell:
He can just push wave all day while harassing you with his manaless ability spam. If you try to gank him, he just shadows away. If you somehow manage to have the upper hand in lane, he can just cs safely with his w+q and can last hit very easily with his passive. If he gets you below 60% hp, prepare to get tower dove and killed while he gets away safely because of his ult. If he is struggling in lane he can just get hexdrinker and eliminate any advantage you had over him. If he is ahead, he can just get serrated dirk with makes him able to 100-0 any time he wants.
Tldr: Zed needs nerfs.