While a child, Robert Lee Henry attended public schools. He graduated from Southwestern University in Georgetown, Texas in 1885 and from the University of Texas at Austin in 1887.
Robert Lee Henry served as mayor of Texarkana (1890-189). Then was appointed First Assistant to the Attorney General of Texas (1891-1893) and Assistant Attorney General (1893–1896). He settled in Waco, Texas in 1895 and practiced law. He was elected as a Democrat to Congress from 1897-1917. From 1905-1907, Rep. Henry was Chairman of the House Democratic Caucus. He was also Chairman of the House Committee on Rules (1912–1917). He ran unsuccessfully for nomination as the Democratic party's candidate to the United States Senate in 1916, 1922, and 1928. In 1923 he moved to Houston, Texas, where practiced law and participated in state politics.
A strong supporter of Woodrow Wilson in 1912, Henry was considered a progressive Democrat.