The problem with League's "Lore" is that it isn't really Lore.
There is no overarching story with League of Legends anymore. Back when the League was an arena to solve disputes and summoners existed there was some semblance of Lore; but I guess they felt that was too hard to keep up with the numerous champions they were adding to the game; coupled with having to have all those champions have a reason to do battle on summoners rift.
They just said fuck it, and now their "Lore" is mostly short story vignettes of these characters; and these stories don't really tie into one another or form a solid, singlular narrative. There is no single main objective for this gigantic cast of characters, but how could there be with 100+ champions?
Speaking of the champions themselves, the writing is very flat and shallow. All of these champions have to be ultra power and/or badass to seem cool in order to get the players to play the champions. There is no mediocre champion lore. Every champion is the best at what they do, and they're complete badasses with ultra powerful spells and suffer little or no setbacks in their lives. This makes for very empty characterizations, and further makes me believe that there isn't any attempt to have a single storyline. Some shit in someone else's story might effect one or two characters, but its very minimal.
This is why I feel that a League MMO would be a boon to the series, storywise. The Lore department would actually be able to craft a narrative, and not simply short stories about ultra powerful characters.