Dillin and Cuidera bring back Lady Blackhawk in Blackhawk 140 (Sept. 59).
While it is still far from clear exactly where Lady Blackhawk lives, in this story we see that she spends her time working as a secretary. When she hears the news about the Blackhawks apparently crashing in the Pacific, she gets into her Lady Blackhawk gear and sets out to find them. In fact, the Blackhawks have been captured by the Scavenger, who has a floating island base, and a ray gun he used to bring down their planes.
Lady Blackhawk finds the island, and the Blackhawks signal her, warning her about the weapon. As seen on the cover, she sends down a decoy to attract the villains attention, while heading down herself and freeing the rest of the team.
Together they defeat the Scavenger. As the story ends, Blackhawk comments that they might get around to voting her honourary membership at some point. No rush or anything. They do it fairly soon afterwards, though, as Lady Blackhawk returns as an honourary member in a couple of months.