Max and Lex

I'm not sure I understand how Maxwell Lord's vaguely defined powers work. I know he can "push" people into believing certain things. He can convince them that things never happened or that they happened in a very different way. The two big examples are the death of Blue Beetle (murder vs. suicide) and the OMAC Project (Max Lord vs. Lex Luthor). My big question has to do with the latter.

If the world thinks Lex Luthor was responsible for the OMAC Project then... Who does Lex Luthor think was responsible? I won't buy that Max can even convince a mind as powerful as Luthor's that he did something he didn't do. That just won't fly with me.

As I see it, the other explanation is that Lex Luthor knows he didn't play a part in the OMAC Project. And that that inconsistency also means that he knows who Maxwell Lord is.

Luthor, of course, doesn't care what Max is up to. He's got his own agendas and couldn't care less at this point what the world thinks of him. He got his pardon and is back in control of his company. As long as Max doesn't butt heads with Luthor there won't be a problem.

Of course, this is all just idle speculation; clearly we aren't going to see any connection between these two stories. But how much fun would it be? After all, Max Lord seems to want to rule the world. And as far as Lex Luthor's concerned that's his job.