Quick questions:
Of all of the champion lore, which lores are actually relatable to anyone?
_Of all of the Champion lore, which ones feature sexuality as a key or core motivation?_*
(*Hint: Lucian is not motivated by his sexuality. He is motivated by loss)
If you are asking for characters to be more relatable to people, then sure, I think many people would agree that some of the backgrounds need more fleshing out and details that make them more individual and unique from one another.
Could one of them fit into the LGBTQ+-X group? Sure.
Is that what you are asking for? I don't know.
So far it seems that you are asking for two things:
-That a character be homosexual
-That a character's sexuality be more than a plot device and instead be his driving motivation
Would there be some issues with some people if there were a homosexual character? Sure. But I, and the majority wouldn't care. There may even be support for it.
Would there be a major backlash from the gaming community and the governments of other regions if the character being homosexual was a driving motivation and central to the character? Oh yes. Without a doubt.
I believe this is where a lot of the "hate" people from the LGBTQ+-X community get comes from. People can generally accept the first thing, or at the very least not be so bothered about it. The second part is where you not only lose people, you alienate them to the idea.
What you are asking for is not only a tough concept for Riot to logistically, legally, and conceptually do, but is something that many people feel doesn't even really have a good example of outside of games like LoL. Riot draws a lot of inspiration for characters from other sources, and there has yet to be one like you are describing that Riot could really work and mold into a champion.