The table was set. The pastries arranged. A white tablecloth dangled placidly in the early morning mist, surrounded by 12 golden-hued high-backed chairs. Five decades ago, a dozen friends gathered here, on the National Mall, for breakfast. They wore morning coats and floor-length dresses, dined on oysters, drank champagne and danced together as a string quartet played in the shadow of the Lincoln Memorial. The extravagant scene on July 19, 1974, drew in a Washington Post photographer, who captured the moment in an image that would ricochet around the country in newspaper reprints. But the people and circumstances at...