The primary issue with AP Ezreal is his lack of reliable waveclear. Against somebody like lux, morgana, malzahar, you are basically pushed to your turret the entire laning phase, scrambling to last hit minions. It's difficult to actually harass your lane opponent at all because of this, and you can end up losing lane pretty easily. It limits your roam potential, and limits your gold income overall. Auto-attacks don't do much, W doesn't hit minions.. E costs so much mana, and his ultimate can't even clear an entire minion wave. The most extreme opponent IMO would be Twisted Fate. His one ability can nearly wipe out an entire line of minions. It's pretty difficult to lane against that.

His W width nerf is pretty noticeable, as well. It would be nice if that was reverted. If he misses that, he doesn't do much damage at all. It also feels like his W doesn't start doing damage until a few points into it.. feels like a waste of mana until then... but if you harass too much with it you'll OOM quickly.

I feel like Sheen getting cheaper on the PBE will help AP Ezreal out a little, though, since Lich Bane is so good on him. But, overall, I used to really love AP Ezreal... but his laning phase is just so awful, and he has few favorable matchups. He can't really be played in any other lane, either.

The best idea that I've heard (but it ends up being a "cheap fix") would be to have his W apply a debuff to minions that it hits, that Ezreal can auto-attack for more damage. Basically, the same thing Lux has. The only down-side is that to apply this debuff, it would have to "hit minions" which would feel strange if it then didn't stack his passive... but stacking his passive on minions would be too powerful, unless he can only generate one stack per ability, from minions.

Bring back old Lich Bane!!!
New Lich bane is an overall nerf to Lich bane users
Champs that didnt do physical damage with on hits usually converted all damage on it to magic damage with the ability (ie mace of spades, urchin strike)
And on hit abilities that did physical damage benefitted from it due to the massive scaling on it, combined with already strong physical damage on the on hit ability.
New Lich bane makes all magic damage on hit abilities weaker, and force physical on hits to being weaker overall form low magic damage on Lich bane, making it mixed dmg.
Weaker overall on most characters.

my favorite part about ap ezreal is that it allows me to sit back and support my team with my heal

I think Ez's W should do 20 - 30% damage to minions. Other than that his AOE damage is pretty high.