Lots of champions do have backgroung story, some of them even have somehow interesting story.

 I just don't care enough at this point, because the whole setting behind the game is unknow to me. I don't know the whole picture, the world where game take place and those little fragment of a story behind some champions doesn't make much sense to me. 

Ayumilove.net have these story when you open the champion page. I am sure there must be a better place where you can read more, but that is the one I know.