Lee Cooksey was born on June 20, 1911, in Harville, Missouri. He enlisted in the U.S. Navy on March 20, 1933, and after completing basic training and advanced training at NTS Norfolk, Virginia, he served aboard the battleship USS Arkansas (BB-33) from October 1933 to May 1934, followed by service aboard the battleship USS West Virginia (BB-48) from May 1934 to March 1937. F2c Cooksey was then accepted for submarine training, and attended the submarine school at Submarine Base New London, Connecticut, from June to December 1937. His next assignment was with the Commander, Submarine Division 4 aboard the submarine USS R-4 (SS-81) from December 1937 to January 1938, and then with the USS Stingray (SS-186) Detachment at the Naval Yard, Portsmouth, Virginia, from January 1938 to November 1940. MM1c Cooksey then served aboard the submarine USS Stingray (SS-186) from December 1940 to April 1941, and the submarine USS O-3 (SS-64) from July to December 1941. His final assignment was aboard the submarine USS Grunion (SS-216) during her fitting out in December 1941, through her commissioning in April 1942, and was killed in action during a confrontation with the armed Japanese freighter Kano Maru on July 30, 1942. On August 22, 2007, a search team organized by the three sons of CDR Mannert Abele (the Captain of the Grunion when she was sunk) used a remotely operated vehicle to find a sunken vessel 3,000 feet down in the Bering Sea north of Kiska Island at the tip of the Aleutian Islands. On October 1, 2008, the U.S. Navy announced that the sunken vessel is the World War II submarine USS Grunion (SS-216).

His Navy Commendation Medal Citation reads:

For meritorious conduct as a member of the crew of the U.S.S. GRUNION which destroyed three enemy destroyers while engaged in a war patrol in enemy controlled waters. Despite severe and persistent anti-submarine measures resulting from these three successful attacks, the GRUNION was brought safely through the counter attacks and continued an aggressive war patrol. As a member of the crew of the GRUNION, your performance of duty was an important and material contribution to the prosecution of this war.