And knowing Lois it's not that hard to believe she would go to those lengths just to satisfy her own curiosity, and see how much more she can find out about Oracle.
That is precisely the problem. Knowing Lois, it's impossible to believe that she wouldn't find out everything there is to know about Oracle. She should have walked into that restaurant with full knowledge of who Oracle is and what she does. If she's heard about Oracle's League connections, she should know Babs is League. If she knows Oracle took down a senator, she should know that senator was corrupt. If she's aware Oracle snuck somebody out of a Mexican prison, she should know who was broken out and why.
And knowing those things, there is no excuse for her to treat Babs like a bad guy. Seriously, what we're looking at here is not a comical misunderstanding where two superheroes from different dimensions meet up, mistake each other for the bad guy due to plausible bad timing, and get some punches in before they figure it out. What we're looking at here is Natasha, on her first day as Steel, coming across Wonder Woman fighting Mongol and attacking Wonder Woman. That massive a failure requires rank stupidity or sheer malice, and I'm not willing to attribute either to Lois Lane.