Its funny, I don't think Lois meant this meeting to be weird if anything I think Lois was going for a mutual establishment of trust with Babs and that Babs messed up mental state due to Katrina is what made this scene awkward.
Lois knows Babs is oracle, you can tell from the get go. She just assumes that Babs knows Clark is Superman and that the two of them can have a nice dinner (maybe relax a little after, damn you SD for making me think like that!) Lois can fulfill what Katrina is after and go home with no harm done. Babs totally over thinks this entire situation and gives that awkward boy on first date vibe which comes through in the narration and the art.