Born in Brooklyn, Lawrence began his professional career at age 17. He played with the bands of Frank Foster, Duke Pearson, Charles Mingus, Thad Jones, and Maynard Ferguson, and was a longtime member of the Tonight Show Orchestra and Chico Hamilton's band.
He also performed and recorded with such pop musicians as Liza Minelli, Blood, Sweat and Tears, and the Spin Doctors.
In 1986, Lawrence helped found the Jazz and Contemporary Music Program at the New School in New York City. Ten years later, he and his wife moved to Israel, where he created the International Center for Creative Music.