Born in Thomasville, North Carolina, Lambeth attended local public schools. He graduated from Trinity College (now Duke University), Durham, North Carolina, in 1916, and later attended Harvard. He joined the Army on January 15, 1918 and saw service in Europe during the remainder of the First World War. He was discharged with the rank of sergeant on July 26, 1919.
Lambeth worked in furniture manufacturing between 1919 and 1930, was elected to the North Carolina State Senate in 1921, and was mayor of Thomasville from 1925 to 1929. He was elected as a Democrat to the Seventy-second Congress in 1930 and was re-elected three times before declining nomination in 1938.
He died in Washington, D.C. on January 12, 1961 and is interred in the City Cemetery in Thomasville.