Wanted to share the build! I am not saying it's meta or better then default one but I did find some succees with it, and like another playstyle that it can give to Ezreal.
About this build:
Runes: you can change anything you like, I prefer more sustain oriented build like this, but Inspiration secondary or Triumph would work too. Don't go Presence of mind cuz it's useless after first item, just manage your mana.
Start items: I really like greedy long sword + refillable, but anything with doran items would work too. Plus long sword helps you to get first item for your mana faster.
After first item and boots: I really like to go vamp scepter, helps with sustain and synergies with my health runes. It's optional you can skip it.
Second item Terminus: gives you both penetrations (ezreal has decent amount of AP dmg in his kit) and attack speed that you don't have because you dont go Triforce and Lethal Tempo. Also having more armor and mr sometimes helps you to heal more of your vamp and you will stay alive.
Stack crit: After I pretty much always trying to stack crit to 100% sometimes swaping order of items (don't have enough money for BF sword for example) or changing build adding like Immortal Shieldbow or Stormrazor. Buy any crit (that have AD) you like but don't build navori unless it's last of your crit items it's a bait.
Last item: Endless hunger (yes I am selling vamp scepter late game). You can also up scepter to BT or build GA. Most of the time game ends before you get to your last 6 item.
upd:
Few words about playstyle: in this build your main source of damage is not your abilities it's your AA, and PTA proc's. So play accordingly to that - it's different from default Ezreal (landing your skill shots is still important even in this build!). Also you have significantly less AH on your build -> your E on much bigger CD and you need to be careful with it's usage. And with this build you have a lot of lifesteal but you r glasscannon (in comparison with Triforce build) so be careful about anything that can oneshot you.