The League Still Exists -.-
I've seen a lot of confusion surrounding this issue, so let me try to clear something up. Keep in mind that I'm no Rito employee, so my words isn't law, however i am a computer scientist, so we can assume I'm right.
Nowhere did Riot say the League of Legends doesn't exist, they said the Institute of War doesn't exist. Before the Institute of War vanished from all existence, it was not synonymous with the League of Legends, it was the sponsor. They were the entity that created and ran the League. Now that they're gone, we're left with no evidence of their time on Runeterra other than their creation, the League. Seriously, do you really think the lore team was gonna take the League of Legends out of League of Legends? Some champions are linked to the IoW, but most our all of them are linked to the League.
What else would
atone for? Where would
and
go to fit in? Why would
, who simply wants peace the Freljord, be fighting? Why is Rek'sai there? (No really, this is kinda off topic, but, I can't imagine a fitting explanation to why she's in the League).