I like Jax, which is to say I ban Jax. let's go with Jax.
Jax is at his very core a champion with unrivaled, sometimes cast as even unlimited power. His nature is to seek out a challenge and overcome it without regard. One could even say he's friends with Gragas because Gragas gives him the bar brawls he enjoys to get by between the league matches. So how does his kit portray this?
I think the best and most kit and lore-kit defining feature he has is F*%@ing DODGE... I'm sorry, I don't know what came over me there. Anyway, his dodge is basically the emphasis that regardless of what you throw at him, he'll overcome it, dodging the blows you throw and coming back even harder as a result. Cast him into the pit of hell, and he'll still overcome.
That still leaves the rest of his kit though, which isn't kinda lorekit friendly in someways. You can say that his q is his expression of superior prowess with such a jackass like move. He posits that he is so superior to you,that unlike Fiora's well conditioned charge, all you are is target to jump to and he'll figure out if he actually wants to hit you before he lands.
Grandmaster's might is in effect his most primal form. He's always ready to dish out damage to any for who can last for more than a second and when a true challenge is put before him, he has a next level to take it to.
Empower is actually a really interesting thing to. Has anyone noticed that a purely martial character is using magic? In a sense, Empower could be said to mean Jax has the ability to unleash bolts of magic and great devastation afar, and yet all he does is smack you even harder with it.
Relentless assault is his reverie for battle, as he fights he loses himself to a more and more base instinct to hit more and hit harder and hit faster and hit more and more and more.
You can basically say that the different parts of his kit reflect two parts of his character. His Q, W, and weapon of choice reflect his ability to do so much more, yet his will to handicap himself if only for the challenge. His E and R are the challenge conquering side to him, where when cast against a great foe, he can go to the next level and persevere regardless. His passive is then the dark undercurrents where he goes from enjoying the challenge to enjoying the fighting, and losing himself to it.
TLDR: Even Jax's kit thinks it's better than you