How to reconnect the Leeague with the new Lore: Champions aren't people, they are Legends.
This whole mess started with the premisse that the League was too restricting to Storry development. And I wholeheartedly agree with that!
It was somewhat annoying to see every character introduction end with a variation of the line "and they entered the League" They are kinda stuck at that point.
However, as you should have noticed by now, you went about resolving it the entriely wrong way. It's actually hard to believe that anyone would even suggest something like removing the League of Legends from League of Legends. Let alone everyone agreeing with it.
You basically removed the entire core of the game and then even had the gall to say "Yeah it's Super Smash Runeterra now, deal with it!" Anyone (except your obvioulsy) could have imagined that going sour.
Well now to the good points: The Shurima Lore we got so far was a good start. I especially like the fact that Nasus and Renekton are part of Runeterra now, instead of some summoned aliens. However Xerath looks flat evil now, instead of the tragic layered character he was before. But Rioters said that's because this event was focussed on Azir's point of view and we'll get the rest of Xerath' story later. So i'll hold my judgedment about that, but I do wonder why it wasn't done now.
So the Lore seems to be going in the right direction at least, but it remains that it is completely detached from the game and that's the biggest issue people have with it. So how can we get the two back together?
Let's see, one of the biggest problems with the old lore where that the champions couldn't really do anything anymore after joining with the League. Well don't require the actual people to be in the League, have the champions be a representation of their Legend.
Like they already did with Baron Nashor: His lore explicitely states that the IoW could find the actual baron, so they made a copy based on his legend. Have them do that for all the characters.
Also people have been comparing the IoW with the UN, but that is not quite right, the UN is based on mutual agreement. The IoW stands above nearly untouchable, enforcing order on Runeterra, that's what's restricting the story too much around it..
Getting rid of the notion that the summoners are all powerfull otherworldly beings (players) was the right direction. However Runeterra has enough powerfull mages of it's own to create the IoW by itself, with a lot more balance.
So by what we have sofar the story would enfold something like this:
Sivir ressurects Azir, who ressurrects Shurima. That and a few other events eventually lead to the great Rune Wars that devastate the entire main land and also draws in the surrounding islands. After a while, some powerfull neutral mages grow tired of the war and join together to force a cease-fire. The IoW is formed and the nations reluctantly agree to resolve the rest of their conflicts on the fields of justice.
Thus drawing the connection back to the game.
That way summoenrs are representatives of the different Nations, using their Legends to fight for their country. This would also allow for those gamemodes like the incredibly popular Ionia vs Noxus game, where the Nations are only allowed their own champions or neutral ones.
In this setup, most of the lore would exist and could freely be resolved before the IoW is even formed, while it still allows Champions like Jax and Orianna whose lore is solely based on the existence of the League.
tl,dr: Riot Narrative goofed (again), lets' try to fix it constructively: A lot of the story unfolds before the IoW is formed. The IoW is formed by powerfull but not allmighty sorcerrers native to Runetrra. Champions are magical beings, created by the IoW meant to represent a certain Legend. The actual source of that Legend does not have to be associated with the IoW (or even alive). Summoners are representatives of each nation that resolve conflicts on the flied of justice.