A few patches ago, Riot decided to scrap the old lore.
The old lore said that The Institute of War was created to bring peace to Runeterra. Powerfull mages known as Summoner's were called in to the Institute of War to help do these matches. We as players were the summoners. Lee Sin also was a summoner, but he got ahead of himself and summoned a boy from a village. The boy he summoned got torn apart by the spell and the feedback of the spell acted as a bomb and destroyed the village, therefore he became a monk. Before the Insitute of War was founded by Reginald Ashram, Noxus (Darius, Kata, Draven) invaded Ionia (Yi, Irelia, Udyr, Karma) and LEe Sin set himself on fire for two weeks (making him blind)
But yeah, they scrapped the idea of Summoners and the Institute of War because every new champion needed a reason to join the League of Legends, why on earth would Gnar and Rek'Sai join there?! Why would Azir, and emperor, fight for some lowly mages?! Questions like that makes each new champion more challenging to make, and therefore the League of Legends was removed etc. to make room for a new lore. So LEague of Legends is basically just a name paying homage to the old days now.