I agree with you wholeheartedly, and I think you should put special emphasis on the weaving of stories.
The rest of this is just my opinion, but I hope we can start a discussion about what we mean by lore.
I think you only touch on the larger issue of story telling for Riot, which is that they are attempting to have a timeline (see Riot Jaredan's quote) rather than timelines. It seems to me that Riot is trying to tell a single overarching story featuring all of their characters, rather than using the narrative devices of a frame story, unreliable narrator, and incongruity, among others. In fact, I think promoting speculation and ambiguity is exactly what they need to do. Nothing (or very little) should be set-in-stone or linear. To quote Thomas Mann: "The well of history is deep - shall we not say that it is bottomless?"
What I mean to say is, everyone seems to think that a character's 'lore' means his or her story, which isn't the case. Lore is, by definition, stories. A body of knowledge, beliefs, and traditions held by a particular group about a particular subject. Our heroes don't all have to 'know' each other, or encounter every other hero in the game, or even exist all at once in the same era. To quote master story-teller G. R. R. Martin, talking about a character from his ASoI&F: "No one can even say for certain if he ever lived. He is as remote from the time of the novels as Noah and Gilgamesh are from our own time."
I think Riot needs to adopt that mindset. It's even in the name of the game - legends. Plural. That's not (or shouldn't be) a reference to the 125+ legendary heroes but the legends about each and every one of them.
Thoughts?