On Thibaud's recommendation Spiller played in freshly based chamber orchestra by Alfred Cortot, along with Zino Francescatti and Maurice Vieux.

[5] On the eve of the World War II, Spiller left Europe to escape, as a Jew, the Nazi persecution.

Spiller became active in a lengthy list classical groups, organizations and related professions, including: symphony orchestra concertmaster for LRA Radio del Mundo and the Amigos de la Musica; conductor, founder and artistic director of the Conjunto de Cámara; associate professor emeritus at the University of La Plata; and conductor and violinist of festival in Córdoba.

Spiller achieved many recognitions: the Sirlin Award in 1971 as the best Argentine professor of instruments in the past ten years; OEA and CIDEM honorary diplomas in Washington; two Konex Awards as a teacher for classical music; appointment as a Consejo de Música adviser to the governments of Germany, France, Switzerland and Austria; honorary member of the Association of Musical Artists in 1985 and of the Henryk Wieniawski Violin CompetitionAssociation in Warsaw.

On the occasion of the Vaclav Huml sixth international violin competition, Ljerko Spiller received the Order of Danica Hrvatska in February 1997, which was awarded to him by Croatian President Franjo Tuđman.