She should have walked into that restaurant with full knowledge of who Oracle is and what she does.
I agree. I think she did know all of that. And I think she still chose to come at Babs that way. I don't think she's sincerely treating Babs like a bad guy. I think she wants to confront Babs, because like Babs, Lois is a know-it-all but arguably has a bigger ego about it, and takes a bit of pleasure in showing off to a woman who is also master of investigation.
All Lois is doing is essentially saying "this is what I was told, this is what I found out--oh hey aren't I great at this?", and because Babs doesn't know Lois personally, she's not in a position to judge if Lois is seriously threatening her or not. It's Babs who makes the situation dramatic and assumes Lois is out to get her.
Another reason why I like this scene is that it demonstrates how formidable both Lois Lane and Oracle are, that they're capable of doing great harm, but don't.