Lore is there to serve the background of the champion.
I have to agree on the part about 'most people don't care about it', but I don't think a story mode will be possible since every champ have very different backgrounds. Some of these champions even have multiple characters that was never introduce to the game (Poppy's old man, Katarina's dad, Annie's parents, Sona's adoptive mother etc.), trying to incorporate all of those into a story mode is nearly impossible especially on a MOBA.
However, I do not think that lore is a waste. Lore might not have a big purpose in term of game play, but they are the source of creativity. Of course there are going to be people that over sexualize these characters regardless of their actual personality. But there are also many piece of arts, that truly show the champions debt and beauty. For example, I would have never understand why
say "Why are they running?" when she is in her idle animation if it isn't for the lore. Apparently, she is a robot that try to hard to be a human that she end up creeping out everyone. "Why are they running?" might actually represent her recalling the memory of children running away in fear when she tried to "be like human", which is really sad that she have nobody that can understand her as a robot, except her dad who has gone crazy at that point.
As for why they are putting so much work on lore, I believe it's there future/back up plan. Let face it, gaming industry is so fast pace, a big thing can die in a matter of seconds in this community. In the future, lore might become a great part of their new products as they continue to grow. Either way, I wouldn't mind seeing an animation of these lore, right now we just have the lore TL;DR, which is... cool I guess.