La Vecchia was born in Rome, and began studying music with his grandfather, who taught him theory, harmony and composition.
In 1972, he founded the Boccherini Quintet, and played hundreds of concerts with this ensemble in Europe, America and Asia.
In 1978, La Vecchia founded the Accademia Internazionale di Musica Arts Academy.
In 2001 he was made Director of the Professional Training Course for Orchestral Conductor Professors, and at this time launched the Ottorino Respighi Youth Orchestra.
Specializing in Italian music, La Vecchia has made dozens of recordings, including the first complete orchestral works of Alfredo Casella and those of Giuseppe Martucci (that was previously recorded by M° Francesco d'Avalos with the Philarmonia Orchestra), both for the Naxos label.