He migrated to New York City in 1905 and became an associate in
neuropathology at the
New York Psychiatric Institute where he was the pathologist at the Manhattan State Hospital on Wards Island until 1913. In 1913, he became a psychopathologist and the assistant director of the Bloomingdale Hospital in
White Plains, New York. He began his career at Columbia and the Presbyterian Hospital in 1922 when he accepted an appointment as chief psychiatrist and director of the Vanderbilt Clinic psychiatric department, serving in the role until 1929. He remained an attending psychiatrist at the Vanderbilt Clinic from 1930 to 1939, was an assistant consulting psychiatrist at the
New York-Presbyterian Hospital from 1924 to 1939, and served as an attending psychiatrist at the New York-Presbyterian
Sloane Hospital for Women from 1929 to 1939. Lambert was an associate professor of psychiatry at the
College of Physicians & Surgeons from 1923 to 1929 and professor of psychiatric education at
Teachers College from 1926 to 1937, where he taught courses on mental hygiene and psychiatric disorders. Lambert advised the military draft service on psychiatric issues during both World Wars and was a consultant on the psychiatric condition of several notorious criminals. At the time of his death, he was semi-retired and served as the medical director of the Four Winds Hospital in Katonah, New York, a private psychiatric facility that he founded in 1925. ==Family==