The thing is, I think you have to allow for a little bit of implausibility sometimes for the sake of dramatic and/or comedic effect. And here I think it's totally worth it.
I mean, yes, it is possible that Lois would just glance across her desk and say "Hey Clark, on a scale of evil to awesome, how would you rate Oracle?" and leave it at that. But that's not as much fun or as interesting as having Lois decide to investigate for herself, to satisfy her own curiosity and not just take someone else's word for it. 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. Especially considering what she dug up about Babs is stuff that Superman probably didn't know at the time.
At any rate, it later gives Lois and Babs an excuse to be allies who know each other's superhero-related secrets, meaning that if they need to work together in future, Lois won't have to BS about where her husband is and Babs won't have to BS about her day job.
(And on a meta-level, I think of Lois Lane and Babs--along with WW and Supergirl of course--as being some of the oldest and most well-known female DC characters. They should know each other, and be friends and allies. And this scene, though it may not result in them being instant friends, opens the door for them being allies, because they can at least respect the other's abilities.)
I do agree that often the "fight first, friends later" thing can be a very thin and crappy plot device, but like I said I think it's worth it here, and not so implausible. Plus it's such a common trope with superheroes, it's kind of refreshing to see it done with superhero characters without a single punch of kick being thrown.