I've come to realize, a lot of the Noxian/zaun champs have something wrong with their left eye, like Kat and Darius' scar, Blitz has a larger eye, urg is missing his left eye, etc. What is with this? "luck" or something else???

In Noxus, they attempt to remove your left eye with a rusty spoon at the age of twelve. If you survive, you are a worthy Noxan. If you keep the eye, they put you in the League.

There's also some kind potion on the left side of the LoL banner :0

You forgot Riven's war paint under her left eye.

Maybe it's some kind of marking indicating weapon mastery or something? Like in the Wheel of Time series, a heron mark is the symbol of a blademaster. Maybe in Noxus a scar or marking on the left eye is a symbol of blade proficiency?

Shaco's shiv hand is closer to the enemies left eye.