Born as Lukas Fuchs (1922-2009) in Berlin, Germany he was soon recognized as a child prodigy. He began piano and theory lessons with Julius Goldstein [Herford] in Berlin at the age of six. His parents were Hilde (Schindler) and the philosopher and scholar Martin Foss. He moved with his family to Paris in 1933, where he studied piano with Lazare Lévy, composition with Noël Gallon, orchestration with Felix Wolfes, and flute with Louis Moyse. In 1937 he moved with his parents and brother to the United States, where his father (on advice from the Quakers who had taken the family in upon arrival in Philadelphia) changed the family name to Foss. He studied at the Curtis Institute of Music in Philadelphia, with Isabelle Vengerova (piano), Rosario Scalero (composition) and Fritz Reiner (conducting).
At Curtis, Foss began a lifelong friendship with classmate Leonard Bernstein, who later described Foss as an "authentic genius." In 1961 Bernstein conducted the premiere of Foss's Time Cycle, while Foss would conduct the premiere of Bernstein's Symphonic Dances from West Side Story.
Foss also studied with Serge Koussevitzky during the summers from 1939 to 1943 at the Berkshire Music Center (now known as the Tanglewood Music Center) and, as a special student, composition with Paul Hindemith at Yale University from 1939 to 1940. He became an American citizen in 1942.
Foss was appointed professor of music at UCLA in 1953, replacing Arnold Schoenberg. While there he founded the Improvisation Chamber Ensemble, which made its Boston debut in 1962 for the Peabody Mason Concert series. He founded the Center of the Creative and Performing Arts in 1963 while at the State University of New York at Buffalo.
Six different years from 1961 to 1987, Foss was the music director of the Ojai Music Festival. From 1963 to 1970 he was music director of the Buffalo Philharmonic Orchestra. From 1971 to 1988 he was music director of the Brooklyn Philharmonic (formerly Brooklyn Philharmonia). From 1981 to 1986, he was conductor of the Milwaukee Symphony Orchestra. He was a professor of music, theory, and composition at Boston University beginning in 1991. His notable students include Faye-Ellen Silverman, Claire Polin and Rocco Di Pietro.
He is grouped in the "Boston school" along with Arthur Berger, Irving Fine, Alexei Haieff, Harold Shapero, and Claudio Spies.
He was a National Patron of Delta Omicron, an international professional music fraternity. In 2000 he was awarded a Gold Medal by the American Academy of Arts and Letters.