Lauri made his debut for Estudiantes in 1928 during the amateur era of Argentine football. He made his debut for the Argentina national team in 1929.
In the early 1930s, after the professionalisation of the Argentine game, Lauri was part of the famous Estudiantes attacking lineup known as Los Profesores (The Professors). He earned the nickname Flecha de Oro (Golden Arrow) for his powerful right footed shooting ability.
In 1935 Lauri played in the Copa América where he scored his only goal for the national team, they eventually lost in the final to Uruguay.
In 1937 Lauri was signed by French club Sochaux-Montbéliard, he was part of the French league winning campaign of 1938.
Lauri played one game for the France A side in 1937 making him one of only four Argentines to play for France.
In 1939 with the Second World War looming Lauri left France and returned to South America, where he played for Peñarol in Uruguay.