Superman dying and why people might hate Supes are, of course, two different issues. And sure, you're right: a person doesn't have to agree that Supes did wrong in order to see how the situation could be twisted
But, I think using MoS as motivation for why people are hating on Supes is a bad idea, as it would just validate all the haters' belief that Snyder, and Supes himself, should somehow apologize for Supes' behavior in that film. I don't like that.
I would much rather see Lex plot Supes' downfall, using fresh incidents in BvS.
This makes more sense and works better, imo, for two reasons (aside from avoiding the things I mentioned above):
1. It shows Lex as a master manipulator in a stronger light if he is completely responsible for Supes' trouble, rather than lamely exploiting prior events.
2. It could tie into a nice secondary villain such as Metallo Doomsday, or maybe even Cyborg, as I think it's possible he might be a villain before becoming a hero.