Ronald S. Lauder, the billionaire cosmetics heir and art collector, will continue to own a well-known painting by Gustav Klimt, which he has held for 50 years, after agreeing to restitute and repurchase the work from the heirs of a Jewish woman who had owned it before World War II. Terms of the purchase, which followed several years of research into the painting’s history, were not disclosed. Mr. Lauder first bought the work, “The Black Feather Hat,” created in 1910, from a Manhattan gallery in 1973, and it has been displayed in several exhibits at the Neue Galerie, which Mr....