Niels la Cour studied music theory, music history, and aural skills at The Royal Danish Academy of Music 1964-69 with Finn Høffding among others. He studied orchestration and composition with Leif Kayser in 1973-1974 and at the Conservatorio di Santa Cecilia in Rome in 1975.
La Cour was active as a teacher of music theory at the Carl Nielsen Academy of Music in Odense between 1968 and 1977 and at The Royal Danish Academy of Music in Copenhagen from 1978, and besides teaching and composing he occasionally works as an organist.
La Cour's list of works range from orchestral works over string quartets to works for solo instruments, but he is mainly known as a composer of choral and chamber music.
He received a three-year scholarship from the Danish Arts Foundation in 1973, and in 1988 he was awarded with "Choir Composer of the Year" by the Danish Amateur Choral Federation.