Born in Boston, Massachusetts and raised in Michigan, Dalitz worked in his family's laundry business early on, but began his career in bootlegging when Prohibition began in 1919, and capitalized on his access to the laundry trucks in the family business. He operated primarily between Cleveland, Ohio and Detroit and Ann Arbor, Michigan. While converting his profits into legitimate businesses, he also owned several illegal casinos in Cleveland.
His investment in Las Vegas began in the late 1940s with the Desert Inn when the original builder of the resort, Wilbur Clark, ran out of money, and Dalitz took over the construction. When it opened in 1950, Clark remained the public face and frontman of the resort, while Dalitz quietly remained in the background as the real owner. He also ran the Stardust Resort & Casino for a time after the death of Tony Cornero. Dalitz owned the Desert Inn until 1967, when he sold it to the billionaire Howard Hughes. Since he had been under constant pressure from law enforcement for many years, selling the resort was seen as an opportunity to get the authorities off his back.
Dalitz continued to be active in the Las Vegas community. When he died in 1989 many organizations received substantial donations he left in his will.