The son of American parents of English descent, Lewis Cohen was born during a temporary family residence in London. He spent his youth in New York. After finishing Columbia Grammar School, he went to Dartmouth College, Hanover, New Hampshire, graduating in 1878. Initially, but briefly, he studied medicine. Ill health caused him to abandon this pursuit and precipitated travel to the Adirondack Mountains in New York and then five years' residence in Colorado Springs, Colorado.
During this period Cohen developed his artistic talents, which had been a youthful pastime encouraged by his mother, who was an amateur painter. In 1884 he enrolled in the Slade School, London, later studying under the Scottish genre painter
J. Watson Nicoll and A. S. Cope, an English portraitist. Cohen also studied with Alphonse Legros in Paris. He lived in Europe for almost twenty years, returning to the United States only for periodic visits.
While living abroad, Cohen exhibited in the Paris Salon and at the Royal Academy, London. Born to affluence, he did not need to secure his livelihood through art. However, his work successfully attracted buyers, and he was known for his generosity to his colleagues.
Cohen returned permanently to New York in 1904, establishing a studio on Sixty-seventh Street. He had first visited Old Lyme, Connecticut, in 1900; after returning to America he spent almost every summer there, finally purchasing a cottage in the area in 1909. The Connecticut countryside and the artists associated with Old Lyme in the early years of the century, including Frank Bicknell and Henry Ward Ranger, were influential in Cohen's artistic development. He turned from figure and genre scenes to intimate pastoral landscapes of the Connecticut countryside.