JLU's Lord Superman was a dictator, but he was the kind of dictator canon Superman would be if he were a dictator, and for the reasons he would be. Justice League Beyond's Lord Superman is a dictator, but he's also a bully, and worse things as well, and in no recognizable way a point B to canon's point A. He's not an answer to how would Superman be a bad guy?, he's just a generic bad guy with Superman's face.
As an aside, Injustice's Superman is not even that. He's just a plot device making whatever bad decision the story requires him to. I understand that the death of Lois and the baby (not to mention Metropolis in toto) twas supposed to crack him, but I don't think that's how his mind works - that's not the way he would crack. Even here, the animated show did it before and better: the world in which Lois died and Superman and Luthor "allied" to protect the city was one in which Superman was a rather oppressive crimefighter, but even then he was still recognizably himself, and the worst of what went on in Metropolis happened without his knowledge, not under his command.