If against a strong killing lane you want to try to farm as much as possible and poke down the enemies with your Q. Once you get your essential items you want to use your range advantage to defeat whoever you are against. You do this by either waiting for a jungler or if you have a tanky support going in yourself.

Try to stay out of the primary damage area and make sure to keep using your abilities(E) to kite any champs or attacks that are aimed at you. Ezreal has a large amount of damage from a range and little hp which makes him best on the back lines. Make sure to use whatever "burst" you have to get the enemies carry and stay safe.

While he is a good adc his Ad may be less than the average adc and you must make sure to know what his parameters in farming are and use your Q to last hit from a distance though you do not want to completely rely on this method because it drains mana early game.

Ezreal works well with almost any support and is quite good with most. some he is best with includes:
Leona
Sona
Lulu
Taric ;P
Thresh
Blitz
Though not in this order and it all depends.

Pros Cons
Poke Can get outdamaged
Kites Can get locked down
Free flash Decent Cd
Can fight at a distance Little hp

Ezreal has one ability that continues to piss people off, he can continue to "flash" and reset its cd using his Q which gives large amounts of damage while running, if the person is greedy and stupid they may continue to follow you use this method of Qing as much as possible and using E to get away until they are low then you may be able to get a free kill. Hopefully you may have a trinity and bloodthirster(lifesteal) and ludicy boots with those three this may work. The trinity with its speed up and massive amounts of extra damage per Q adds a large percentage of success. The Bloodthirster is useful for its ability to heal you as your going because you may be caught out once or twice. The boots are useful for the cooldown reduction it helps you use Q more and E more not to mention the needed speed.