De Lancie was born in Berkeley, California. Starting in 1940, he was principal oboist of the Pittsburgh Symphony Orchestra under Fritz Reiner. In 1942, he enlisted and served in the US military during World War II, performing with the US Army Band. He met Richard Strauss during his tour of duty as a soldier in Europe at the end of World War II. De Lancie knew Strauss's orchestral writing for oboe thoroughly and asked the composer if he had ever considered writing an oboe concerto. The composer answered simply "no" and the topic was dropped. Six months later, de Lancie was astonished to see that Strauss had changed his mind and was indeed publishing an Oboe Concerto. Strauss saw to it that the rights to the U.S. premiere were assigned to de Lancie. However, de Lancie had joined the Philadelphia Orchestra in 1946 as a section oboist, so that as a junior member and under orchestral protocol, he was not able to premiere the concerto since Philadelphia's principal oboist, Marcel Tabuteau, had seniority. De Lancie then gave the rights to perform the premiere to a young oboist friend at the CBS Symphony in New York, Mitch Miller, who later became famous as a music producer and host of a sing-along TV show.
