The League was supposedly a United Nations-esque organization with the sole purpose of stopping war on Runeterra - a purpose for which they shelter known criminals, bind Eldritch Abominations, employ Omnicidal Maniacs, interfere with off-world civil wars, kidnap benevolent extra-planar guardian entities, lure newly sentient creatures with promises of knowledge, recruit the experienced soldiers in the world (and small children) and then make them compete in the most brutal Blood Sport in the world. On top of that, despite supposedly being the final arbiters of justice on Runeterra, they are willing to forgive their own members for atrocities that should be considered gross personal incompetence worthy of dishonorable discharge at best, and horrific war crimes at worst.
Kinda glad they aren't canon anymore :P