Pre-rework Trundle had one of the best backgrounds. :(

Anyways, League and other moba's are in a good place for not having a story mode. Trust me, I love a great story mode as much as the next guy but F2P story modes seldomly convince, even with the amount of work Riot can bring up. Making a story mode would be like making a new game, since none of the game modes right now can relate in any fashion to something like a story mode or any kind of campaign. Also LoL is as stated above a moba. You can't make a moba a continious game.
In addition to all of that, LoL is practically co-op as it is, with people joining together to form a team which needs to play together to win.

For example if you look at diablo, it IS the story mode. Now if you take a moment a see how long it took them to make that game (I won't go into weather or not the game is good since I haven't played it, huge Titan Quest supporter on this side), you'll recognize that something of this scale is sheer impossible without a huge group of people working on making a story mode, and in this case it'd just be easier to make a new game rather than advance LoL. Then again supremacy is coming out quite soon, and it's supposed to be a standalone game so I might be wrong.

Thresh's lore is pretty cool.

I think it'd be cool if they made a graphic adventure game for a few of the champions. I can imagine one for like Katarina, Thresh and Annie etc People with unique or interesting lores :P

That would be great if their lore didn't suck balls and made actual sense.

would be cool to see the lore played out like that, but if it happens it ain't going to be anytime soon.

Would be funny to have something like it tho. The end boss would be like, a super powerful summoner that summons a baron every second where each baron has 10necks with 10 baron heads. Would be epic :3

But yes, probs never gonna happen.

they are busy fixing euw.
seriously though, i highly doubt that they even have enough time for a ****ty story mode.