Doesn't really matter. We know Lois did, since she mentions it here.
Actually after all this discussion it strikes me that that line right there is what's killing the scene. Take it out, and the whole thing makes perfect sense: Oracle hijacks government satellites, has ties to the Suicide Squad and all kinds of known felons and mercenaries, regularly commits fraud, wiretapping, theft, money laundering, etc etc. And the heroes and friends she works with are good guys - they're likely to respect her desire for secrecy and never talk about her. Which means the people who are spreading the Oracle rumors are the ethically dubious hackers she recruits or killers she hires or government agents running investigations on her activities. It is quite possible, perhaps even likely, that someone, even someone as sharp and intelligent as Lois, could investigate Oracle and discover only evidence and activity that paints Babs in a bad light.
And if that happened, this scene makes perfect sense. Lois is on the attack because she genuinely thinks Babs may be a bad guy. She needs to actually talk to Babs, get a read on her, to figure out what kind of person she is, and it's the dinner that convinces her that Oracle's not an appropriate target. (Obviously not because of anything Babs says or does, but I'll buy Lois as that good a reader of people.)
The problem is, the instant Lois mentions in her own dialog that Oracle is rumored to have JLA connections, that interpretation gets completely blown out of the water. It's simply not possible that Lois could have come across that and failed to follow it all the way to the bottom, so that single line demands she came to dinner with full knowledge of Barbara's moral allegiance, and the scene stops working.