Lee was the son of Richard Carrington of Virginia and his wife, the former Sarah Gurley of Pickens County. He graduated from Southern University in Greensboro in 1890 and entered into practice in 1892.
Bradley was appointed assistant Jefferson County Solicitor in 1893 and then promoted to Solicitor in 1896. He married the former Eleanor Lyons of West Feliciana Parish, Louisiana on June 24 of that year and had two children; Lee Jr and Thomas.
In 1898 Bradley and his former assistant Hugh Morrow joined in the law partnership of Bradley & Morrow. Morrow quickly left to join Walker, Tillman & Campbell, leaving Bradley to share an office in the Chalifoux Building with John C. Forney. In 1904 Bradley and William Grubb followed Morrow into the firm of Walker, Tillman, Campbell & Morrow to form Tillman, Grubb, Bradley & Morrow. Bradley remained with the firm, a predecessor to Bradley Arant Boult Cummings, until his death.
Bradley was appointed by President Woodrow Wilson to serve as counsel for Office of Alien Property Custodian, created by his executive order in 1917. He personally lobbied Senator Oscar Underwood for legislation allowing the office to promptly sell, rather than store, perishable goods taken from enemy nations.
Between 1918 and 1921 Bradley's former law partner, William Grubb, appointed him as receiver of the assets of the Birmingham Railway, Light, & Power Company. He helped to organize the Birmingham Electric Company to receive those assets. Bradley also served as a director of the Birmingham Savings Bank & Trust Company and was an organizer and stockholder of the Birmingham Baseball Club. He was also a member of the Birmingham Country Club.
- "The Imposing Residence of Mr. and Mrs. Lee C. Bradley, at Idlewild." (December 5, 1915) The Birmingham Age-Herald
- Lee Bradley at Findagrave.com