Löb became personal liable partner with Mendelssohn & Company in 1919. Following the death of Franz von Mendelssohn and Paul von Mendelssohn-Bartholdy in 1935, Löb was appointed as chairman of Mendelssohn & Company bank as the first non-family member. In the 1930s, he served as the Belgian General Consul in Berlin.
In 1938 he was pressured by the Nazis" Aryanisation policy to break up Mendelssohn & Company and hand over most of its assets to Deutsche Bank.
Löb emigrated to Argentina in 1939 and to the United States in 1948.