So since the League of Legends isn't just a computer game here, there are a few key differences I would like to point out.

-There is no such thing as items. Infinity Edge and Trinity Force and Blade of the Ruined King do NOT exist. Why? Because the Champions are actual people, not just game characters. They have their own weapons. Ezreal has his bow. Lux has her wand. They already have their own weapons and items that they use. It wouldn't make sense for Ezreal to run around with an actual sword.

-Because there are no items, there is no gold. Well, the Champions earn money that they can spend on a daily basis for competing in the League of Legends because it's like a sport, but what I mean is you don't get gold to buy items in a match. Because there aren't items, so gold isn't needed. It wouldn't make sense.

-HP and MP are not things. They are not game characters, they are humans. They die when they die, not when they run out of HP. They can't use spells and stuff anymore when they run out of energy and can't go on, not when they run out of MP. Like I keep saying, they're humans(er, actually not all of them are human, so...they're real I guess makes more sense), not game characters. So no HP or MP.

-Cooldowns are not things. The spells and stuff that the champions are using are their personal abilities. If Ezreal wants to shoot as many mystic shots as he can all at once, nothing is stopping him from doing that because it is his ability. Basically, just don't think of this as the game. Two abilities can collide and make an explosion, because in this story it's all real.

-Minions and Experience and Levels WILL be a thing because it's necessary in order to add flavor to the League of Legends. It'll be explained in a way that makes sense in the story.

TL;DR: Just keep the mindset that in this story, the League of Legends is real and not a computer game. Therefore, anything that exists in the game that only exists to make it a game does not exist in this story. Imagine that the League of Legends actually existed in today, in real life. That's all you really need to know.