Zilean into poke bot lane

Hello guys, im learning zil in plat/em elo and I notice I struggle playing into poke bot lane, like lux&cait or vel&mf or zyra&ziggs. All they do is perma poke by punishing my weakness early and i cant contribute amazingly well to the 2v2 till im 3/6, but that point its tough because my adc is behind and we've died at least once or twice. By the time its late game, we are alot of gold behind and games just oger.

Any tips?