Lore: How to 'fix' Kayle and Morgana without ruining them.
I don't think lore has been such a big subject for so many people in League since, well, ever. With the removal of the Institute of War, the Summoners, and the whole idea of the League of Legends, a lot of characters are going to need tweaks to their lores to make them compatible with the new setting. Among these are two of the most interesting, most detailed, and most popularly-debated characters in the game, Kayle and Morgana. Since they are so tied in with the League one would think they need a lot of changes, and thus that the characters they know and love (or hate) are going to be retconned into oblivion. But in reality, you don't need to change anything about them to completely remove the League from their stories.
Right now, what does the League for these two? It provides them a reason to put their warring on hold and be on Runeterra, considering they're from another dimension by default. It also provides Kayle a secondary motivation in looking for Reggie Ashram, but that has never really mattered to anything. So all we need to do is come up with another reason they'd want to come to Runeterra. The answer is simplicity itself since their existing lore lends itself neatly to it.
For the unaware, Morgana initially approached the off-world Summoners and asked them for help fighting Kayle, as Morgana was slowly losing. They agreed, in exchange for her service to the League for 1000 years. When their help swung the tide of battle the other way, Kayle made them the same offer in exchange for their backing out of the fight again, which they accepted. The League gained two champions and lost nothing. Clever of them!
Suppose, however, the League didn't exist, because right now it doesn't. Morgana, still on the losing side of the fight, hears tales of this fabulous place with all these heroes and champions, and thinks she can rally them to her cause - She realizes she needs outside help or she's probably screwed. So she goes to Runeterra on her own accord to try to drum up support. Kayle, seeing the inherent danger in letting Morgana's voice be the only one this other world hears, decides to follow her and try to gather some allies for her own cause, or at least stop Morgana from getting any. Now we have both of them in Runeterra, with a good reason to be there, and absolutely nothing has changed about either of their characterizations or backgrounds. Simplicity itself.
But perhaps you want to build stories off them, have them interact with the world, so you want to make them native to Runeterra. This is a mistake. Kayle and Morgana being extradimensional actually gives them even more chances to interact with and expand upon the world - Namely, since they're trying to sway support and opinion in their favor per the change above, they have reason to interact with every major faction, something no other character has right now. Further, they ultimately owe little allegiance to the world's affairs and politics. It could easily be a major plot point whether, in their mutual hatred, they'll wind up bringing their war over to Runeterra or not, since there's no longer a League to stop them from doing so. Further, what about back home? Will their war continue without them, or is it possible both sides, after dallying a few years without their leaders, collectively say 'This is bullshit' and settle down to peace talks without them? Now they'd be forced to interact with Runeterra as they may not exactly be welcomed home - Their own people may very well tell them to stay in time-out until they can get along and play nice. Do they ever reconcile? Or do they just look for new proxies to keep fighting their war?
You don't need to completely retcon a backstory to make it 'new' and interesting again. I hope Riot doesn't fall into this trap when reworking Kayle and Morgana, since that would rob League of one of its truly interesting, morally ambiguous rivalries. Presented here is a way to avoid doing just that, and I hope Riot heeds this advice when they go over the older lores and reimagine their world.