He studied at the Royal College of Surgeons in Dublin, but, having almost finished the course, he left and enrolled in the Royal Dublin Society School of Art. He began exhibiting his paintings at the Royal Hibernian Academy in 1880. In 1883 he entered the Académie Royale des Beaux-Arts in Antwerp, where he lodged with his fellow student, the painter Roderic O'Conor, and studied under the Belgian painter Michel Marie Charles Verlat. In 1885 he briefly studied in Paris under William Adolphe Bouguereau, before returning to Dublin the same year, where he established himself as a painter of portraits and street scenes. He was awarded associate membership of the Royal Hibernian Academy in 1889, became a full member in 1890, and remained one of the RHA's most popular exhibitors until 1903. He was also the principal cartoonist of The Union, a unionist newspaper, signing his work "Lex".
- Theo Snoddy, Dictionary of Irish Artists: 20th Century, Merlin Publishing, 2002
- Maebh O'Regan, "Richard Moynan: Irish Artist and Unionist Propagandist", Éire-Ireland 39, 2004