Yeah, sorry, Bluefall, but you have this absolutely wrong from the word go.
I wrote Birds of Prey for five years, I know what Superman's connection with Oracle was. She had not outed herself to to him, although they strongly suspected he had guessed. Lois gets a story about Babs, how in god's name would she know Superman would know her? The story she gets came from a suspect source, Spy Smasher, who introduced Oracle as a terrorist, basically. Where in the world would she come up with "a JLAer named Oracle," when all the info SS gave her was some ambiguous "ties to" connection, nothing even remotely suggesting membership? Where did you get the idea that Lois would think she was a member?
And here you have two of the characters best at keeping secrets in the entire dcu: Superman and Oracle. Superman would not reveal Babs' secret id to Lois even if she had some evidence. He wouldn't compromise her like that. And even if Oracle was in the JLA and Lois knew it, does that mean she'd ignore a tip from a major government source just because Clark thought she was okay?
Finally, how do we know she DIDN'T ask Clark, and went to that meeting to warn Babs to be careful of the precipice?
Where are you getting the idea that Lois would know Oracle 'keeps the world safe?' There's nothing canonical to support that at all that I'm aware of. At that time, Oracle was still meant to be a rumor to most people, CERTAINLY Babs would want to stay off Lois' radar.
The point of the exchange is clear, here. Lois did the legwork, and decided that she wasn't going to be played by Katarina Armstrong, or anyone else for that matter. It baffles me how you come up with 'douchebag' out of this situation.
WE, as readers, know these two women are honorable. But THEY each have reason to distrust one another. That's the ballet they're dancing. Each one can pull the other down. That they choose not to do so is what makes them interesting.