There are a fair number of issues with creating a "Campaign mode" for League of Legends - the first of which has already been discussed in Jeddy017's comment string, which is that a single-player campaign mode wouldn't really mesh well with a game whose core aesthetic of play is competition.
Which, you argue that League's roots in Warcraft give it the wiggle-room to have a single-player Campaign, but...No. Sorry, but, no. DOTA, and, to the same extent, League, are meant to be Battlegrounds. That's why the genre the mod spawned is called "MOBA" - Multiplayer Online Battle Arena. The core aesthetic is a competitive arena battle, not a solitary story piece.
You also say that they should make a Campaign because of the existence of lore - which, unfortunately, is not a really solid argument. "There is lore, so why not?" Doesn't hold up when the lore is only just there, ever-so-slowly being written in. We only have the vaguest sense of the locations in Runeterra, with most of the lore orienting around the culture and aesthetics of a given Faction. There aren't any maps (save the Medarda Heirloom), so we don't know the locations we'd be trekking over in the campaign(s).
Second - You propose it as a way to "learn the mechanics of Champions" - but how would a Campaign mode do that better than Co-op Vs. AI or even PVP already does? You can already learn Champion mechanics just by playing the game, and the mechanics you learn in bots/PVP are applicable to all modes, so...I'm not sure how a Campaign mode would teach you any better.
And, if it's meant to teach you mechanics, then that brings up the possibility that the Campaign just becomes a glorified Tutorial. (which, a Tutorial already exists, so, that space is already kind of encompassed.) Have you played World of Warcraft: Legion and gotten through your Artifact Acquisition quests? Notice how they're all literally glorified Tutorials on how to play the role?
Healer spec items have you thrust into a scenario with one or more NPC's to heal, and you're expected to play through a scenario that only teaches you how to top off teammates and spam your abilities? Or tank specs have you in scenarios with one or two NPC's - one healer, one damage, and you're meant to just taunt-spam and run your defensive cooldowns 24/7?
That's essentially what would happen if the campaigns focused on teaching mechanics. Granted - Riot is extremely good at what they do, so they might manage to work a way around that, but it is still a major pitfall to be had with "learning" campaigns.
Third, there's the issue that, League of Legends has nearly One-Hundred and Forty Champions. There would have to be either individual Storylines (since each Champion has their own unique mechanics, and you did say it should be to teach mechanics, right?), or it would have to be a scant few distinct storylines focused around a very specific few Champions, which would increase the difficulty if they're trying to teach roles. (try and find a Noxian Support. Just try.)
These are just a few issues off the top of my head - but they are very glaring issues with the concept of a "Campaign mode" for League.