The issue with getting closure on a lot of these stories is that the way they were written, any "closure" would just end the story.
Like, with Rengar and Kha'zix...one of them kills the other one. And then what's left for the survivor? Not a ton, because there are so many champions built around rivalries. Even with the game/lore now separated, League tends to cling pretty tightly to the status quo. Likely because making substantial changes to a character in the Lore would usually warrant similar changes in the Gameplay, which costs a ton of resources. You can say they don't have to do that, and it's true, but people want it. There's a topic on this page right now about Miss Fortune's VO not matching her post-Burning Tides characterization. That's not even going into the fact that a lot of these stories would likely end with a character dead, which would probably piss off huge swathes of the fanbase.
Of course, Riot's proven they can get around that in the past, so there's certainly hope. Twisted Fate and Graves actually had their conflict totally resolved in Burning Tides, and it was great, because that was the first time that's really happened in League, and they managed to give them a new story hook to keep them relevant.