He studied medicine in Paris, where he was a student of Joseph Babinski (1857–1932) and Pierre Marie (1853–1940).
During World War I, Léri was in charge of diagnosing soldiers with battle-inflicted neuroses.
He was the author of works in the fields of neurology, ophthalmology and psychiatry, but is largely remembered for contributions made in osteology, particularly in his research of bone disorders.
He described a type of mesomelic dwarfism combined with deformed forearms, which was to become known as Léri-Weill dyschondrosteosis.
With Pierre Marie, the "Marie-Léri syndrome" is named, which is a hand disorder caused by osteolysis of the articular surfaces of the fingers.