It seems like this is going to be a Doomsday created by using something of Zod's, either his DNA or his corpse, and manipulating it in some way to produce a DoomZod of a sort. That particular take isn't canon, but there have been versions where Lex discovers/releases Doomsday, so this isn't a massive stretch. And since Doomsday's origin is that he is a Kryptonian life form of a sort it does make a certain amount of sense, although it does appear that they're mixing Doomsday with a "normal" Kryptonian in terms of him having the heat vision, which he doesn't normally have. As far as being canon, there are various elements of this version that are pretty much identical to some ways he's portrayed in other source material. Using Zod's body is the biggest addition that isn't canon though, but his general appearance and that he's an evolving, adaptive and genetic killing machine - that's all standard.
It's also unlikely this will go the same way as the Death of Superman arc, it's the most famous Doomsday source material but in other confrontations with Doomsday Superman doesn't necessarily die, so the myth that that's the "only'' way to use the character is fallacious.
As far as why Supes acts evil, we see Lex with Lois at some stage, it's possible Lex kidnapped her and his forcing Superman's hand in some way, but that's all up for speculation.
