A renowned teacher of viola, Fuchs was also an important teacher of chamber music, counting among her pupils Isaac Stern, Pinchas Zuckerman and Dorothy DeLay. Lillian Fuchs's influence can be seen in her two daughters, Barbara Stein Mallow, cellist, Carol Stein Amado (deceased), violinist, her granddaughter, Jeanne Mallow, violist, and grandson, David Amado, conductor.