Lumley Graham was born in 1828 in London, England. He joined the 43rd Light Infantry Regiment in 1847 (Ensign 1847, Lieutenant 1851) and served with them during the Kaffir War (December 1851 to September 1853).
Graham was promoted to Captain in 1854 and served with the 41st Regiment during the Crimean War (1854-1855). He attained the rank of Major (on half pay) in 1856 and served with the 19th Regiment (1858) and the 18th Regiment (1865). He was promoted to Colonel in the late 1860s.
On the 2 May 1875, Graham succeeded his brother as 4th Baronet and the following year he retired from the army. He died as the result of a carriage accident at Arlington Manor, near Newbury, in October 1890.