How do i lane against someone who runs ignite/exhaust in top lane?

Firstly, the jungler should pretty much camp the crap out of this lane.

If not, you should treat it as a complete farm lane - so just focus on farming / sustain. If they're playing a really strong all-in champ, you should build defense early so you can survive a full combo at least

It depends on who you are, and who you are against. In general, though, don't commit to a full fight when their summoners are up. Exhaust/Ignite will cripple your ability to duel successfully. So options are to either bait out the summoners and disengage to wait them off (which can be tricky), farm fest it up, or poke them down until you can commit to a duel under the exhaust/ignite cripple.

If you have teleport, popping down to another lane to get some kills or assists can give you the edge you need to fight successfully. Just be careful because your opponent will probably push the lane hard when they see you somewhere else.

If you run flash, you can use this to disengage once they blow their summoners' or re-engage once they wear off.

Above all else, play it safe. The lane phase may end in a boring draw, but if you fight and die a few times, it'll be much harder for your team in team fights. Almost any fed top laner is a terror later.

Tell your jungler to come and pick up the free 300 gold. Even if you dont kill him in a gank you will likely force him to back atleast which will cuase him to lose alot of farm and xp since he doesn't run tp.