Here's what they should do:
Divide all of the characters into their respective factions. (Void creature, Demacia, Noxus, Piltover, etc.) and make a single campaign for each and every one of those areas. They will all have an ambiguous villain or form of evil, an invasion of Demacia - a spy in Noxus, things like that. And the campaign will have different "flavors" depending on character.
An evil mastermind intends on enslaving everything within the void... play as Cho
and you will have levels where you eat things to get stronger, play as Vel'Koz
and you must acquire knowledge to outsmart your counterpart.
The different flavors from the campaign allow champions to gain character as well as promote replay-ability - perhaps even getting some cooperative play at times along side challenges!
The reasoning behind this factional view of the campaign is so that the bits and pieces can be developed a single unit at a time. When creating this campaign, you don't have to worry about cramming 121 champions into it, and you don't have to fret about what kind of tutorial you're going to need to do things - just make all of the Freljord champions in the Freljord story.
Freljord story: the watchers have returned! Or have they? We don't know, but people are scared! Investigate! And through the 7-11 hour campaign, you'd discover that it's all a hoax, only for the watchers to actually be a threat regardless! Play as Ashe
with aspects where you lead people and govern them. Play as Lissandra
and you terrorize people and seek to free the Watchers! You can play over and over if you want, and perhaps make it so that completing that story with a character will give you a skin!
Think about it. pay $30 or so. You get 10 hours of campaign single player, and a free skin for every person you beat it with. Think "Leader Ashe." or "Watcher Lissandra"
Only let them play the campaign with champions that they have unlocked (Or the free ones that week) so that they have incentive to go out and earn/get those champion!
They can crank out these story rich campaigns with ease and will be richly rewarded through it. Release a story mode for demacian heroes and give all of them a skin along with challenges? It drives up the value of League while also making some money! It will also win them over a lot of favor in the eyes of the media. Until they make something like a episodic story mode, then they will be a company that's all about the MOBA - all about the niche. Widening the net is like adding more honey to the fly catcher - more people will be interested and more people will try it.
Cha-ching. Money.
Make episodic dynamic campaign mode + skins and release it as DLC. If you write it well and make it as epic and lore rich as you do humorous and clever - then you'll make a killing and become a legend approaching Valve Status.
Ill write the stories for you, Riot, just message me 