Gragas enters Beer Drinking contests, and goes to all the booze festivals.

Singed Enters Chilli and beans eating contests, You think that Gas cloud comes from his bottle ?

Nidalee is a pole dancer from what i hear, and if you dont pay her enought she goes all cat like on you.

Teemo volunteers as an assistant scoutmaster for troop 338, Simon Kenton council in Ohio.

That's where I first met him 10 years ago.

I did.

Mundo is low hp! throw your championball! O****HEULTE-

I'm thinking Warwick cries in a cave because he wants to be human again... poor Warwick!

And Annie, well she is always at Tibber's/Pedobear's house

It sounds mostly like they do live their own lives, and that the League has an actual entity within the world. So, you get things like Ezreal who runs around exploring and only fights in the League because the gauntlet that gives him his powers also gets him dragged into it, whereas Jax appears to be a "professional" Leaguer.

If you were a champion - a legendary figure that is a hero to some and a villain to others - what would you be doing with your time?

Each champion has their own unique set of circumstances that are independent of the League. Some champions are more closely tied to the League than others. Cho'Gath, for example, doesn't spend much time chilling at the Institute of War; Ryze, in contrast, spends a good chunk of his time at the Institute, honing his magical prowess within the Institute's vast arcane library. Some champions have a very busy schedule that is completely independent of the League. Teemo is quite busy scouting the wilds around Bandle City, keeping it safe from intruders.

TLDR: All champions have lives independent of their time in service to a summoner.

When the call for service to a summoner comes, however, every champion is bound by the following fact: they are ready, willing, and able to assist the summoner who calls upon them in a Field of Justice. The very power of the League - and the fragile tranquility of Runeterra - depends on this.

After this, the champions are whisked back to wherever they were before the summoning.

The hell she does.

D:
i've been living a lie!

From my understanding of the book that came with the box game. They get sent back to their home (or at least their home on Runeterra). They come to the league and sign up to allow themselves to be summoned so the summoners from the different factions can settle arguments and then they are sent on their merry little way.