User blog comment:Nelraye/Lore Discussion: Riot, what happened?/@comment-5116121-20140221204513

You forget that the League gives many opportunities to those who join it. IMO explanation:

Syndra. "More, I need so much more!". Institute of War is the place, that has the most powerful sorcerers in the universe, and, therefore, knowledge and power. Syndra can participate in League not only for entertainment of the crowd, but, as a reward for her services, she can get access to the knowledge. And knowledge is power.

Yasuo. As Iffem mentioned, Yasuo seeks the true murderer. And League's mages can provide assistance and cover from the assasins.

Thresh. He could be kept here to be in check. To be secretly studied at the Fields of Justice. Studied not only by summoners, but by Lucian as well, for example.

Lissandra. League is influence. League is politics. Why fight if you can gain influence and submit everyone to your will without bloodshed. And she can just trick everyone. She is an ancient evil, and I doubt that she has mastered only the ice magics. Another guess, she can just reveal herself and go like "screw this cover, bow to me!".

Well, not failproof, but sorta acceptable. IMO, of course.