Stay behind minions and you can stay in lane with him. His grab isn't unavoidable and unless he's kinda close to you, you should be able to avoid it a decent amount of the time. Although if he's really good he can kinda zone some supports and there's not much you can really do about it. Poke him as much as you can get away with early in order to try to get ahead. But really, if he has to chase you too far to grab you in lane, his grab shouldn't be an instant kill. Keep your hp high by using healing pots and it should be a lot harder for him to kill you. But do ward since if he grabs you and they have an extra champion ready to jump on you, it's really hard to get out. However, if you get too far behind there may be very little you can do anymore.
Some abilities like Morgana's black shield can also make him almost completely useless.
If you really can't figure out how to position to avoid getting grabbed, you could also try watching some videos of how really good players deal with laning against him. But be warned, if your adc isn't very good, you probably can't get away with some of the stuff that you should be able to. So you probably can't get away with doing exactly what they do but it should give you some good ideas.
For counterbuilding, you can try getting some more movespeed. The faster you can move, the less he can zone you. Also if you get something like Frost Queen's Claim or Talisman of Ascension, then you can use that to escape if needbe. Or banshee's could probably really mess his grab up but that's more of a lategame thing that you shouldn't disrupt building your core items to get. I also recommend using a very tanky rune page against him. You can get armor quints, health yellows, mr blues, and if you still want to be tankier, you can also run armor reds.