Wow, Superb, your nightmares mirror my own xD
I think one of Veigar's selling points is the 'at the Edge of villainy or non-villainy' status he always has.
He wants to be a bad guy really hard, amasses power and crafts evil plans, but they always fail at their execution, pushing him back onto the Edge again. His own drive towards evil gets stabilized by outside interference, without fail.
And I love it.
Because there isn't many champions you can weave so many ideas around, at least not without AU's - and it's all because of that Edge.
He's basically standing on the crossroads.
You can just take him, tip him into a spiral of madness and imagine the destruction he'll cause. You can drag him kicking and screaming into redemption and try to see how (and if) he'd struggle to get better. You can imagine his emotions, his thought process. You can grant him everything he's always wanted and see if he's truly happy, and so on, and so on. So many possibilities.
Xerath doesn't have this many. Diana doesn't have this many. They've both done things that cannot be ignored, setting them on a particular path. But Veigar? For now, he has his infinite, status quo Edge, and the Edge can keep the ideas for his development coming in, forever.
The thing is, Lulu is one of the most contributing things to his Edge. Teemo can also count for ruining his plans on the spot whenever he approaches the moral event horizon, but he is only a quick fix without much chance to become more. Lulu is the one commonly believed to have that long term therapeutic effect Veigar needs to balance his evil ambitions and loneliness and keep from falling into the pure darkness. She is also sometimes potrayed as his chance to become good, a morality pet.
She helps him keep his Edge, and many, many people can see it.
Of course, he gives her more Edge too. Under his influence, she often becomes just a lil' bit more clever and wicked, gets dragged out of her daydream and into the adult world, and has a chance to anchor herself somewhere insted of wondering about by herself.
Ever since Riot applied the friendship onto those two, the community view shifted from 'he's not an overlord because he's incompetent/butt monkey' to 'he's not an overlord because he gets distracted by Lulu, probably breaking into his evil lair to give him a cupcake' People got used to the idea they were friends and started relying on it. Hell, I'm relying on it right now xD
Because it's adorable, because it makes sense, and because it compliments the characters in question and gives them more Edge.
And now... Now imagine someone making a quick patch and erasing that entire relationship.
That would be... That would be a low blow.
and 
's friendship on the grounds that it was holding him back from committing true acts of villainy and would be required to move his story forward.
) as opposed to stereotypical 
