I beat him with zyra them plants so stronk ^^

Or Akali. Easy kill, especially since most Zed's don't build hexdrinker first.

I was under the impression zed had a weak laning phase until he got his ult.

buy chain mail and tabi. Once you hit the break point where he cannot 1 shot you, he will stop attempting to jump on you and go roam other lanes. Zed needs kills to scale into late game.

zed is destroyed by a good kayle

A shuriken maxing zed is impossible to "beat" in lane, he can clear waves from range with wqe.
You have to jump on him the moment he uses his W