Lois is someone who is arguably keeping her own light under a bushel for the benefit of others and is taking the opportunity to show off to a member of the cape community that she's not just Superman's wife.
In many ways, she's using a play from the Bat-clan with lots of veiled threats and showing of ominous bulges and demonstrations of the cachet of her own name. I think it would have been more impressive for her to have simply confronted Babs in her own territory without the mind games.