Herbert Lust’s career as an art collector began, as he put it, with a “cock and bull story.” In 1949, Mr. Lust, a 22-year-old American in Paris, found himself at a luncheon filled with artists and intellectuals. Feeling out of his depth, he made up a story about being a Romanian Jew who had crossed the Carpathian Mountains — barefoot! — to escape the Nazis. One of the other guests, the renowned sculptor and painter Alberto Giacometti, was intrigued and invited Mr. Lust to drop by his studio.