The sad thing is that there's nothing about this scene that doesn't make Lois look like a Bruce-level self-aggrandising jerk. She's basically got a whole bunch of stuff she can't tell anybody that the dirty guttersnipe part of her desperately would like to -- "I'm married to Superman!" being I imagine first and foremost -- and is effectively taking it out on Babs in what comes across as an unwarranted pissing contest that seems to be as much about compensating for hiding her light under a bushel for the benefit of others.
There's no other reason for her to pull the restaurant stunt; she's trying to demonstrate that she has her own cachet as something other than someone's wife, that she has weight and influence based on her own abilities.