Dewey was born in Des Moines, Iowa on May 19, 1901.[1][2] He married Florence Powers and they had four children: Lawrence Russell Dewey Jr.; Florence "Cici" Powers Dewey (Mrs. Francis J. Hughes); Donald Herbert Dewey; Elizabeth Hazard Dewey (Mrs. Christopher L. Vance). Lawrence Jr. also became an officer in the military.
During World War II, Dewey served in various positions with the 1st Armored Division, including Chief of Staff.[1] After the war, he attended the National War College, graduating in June 1947. He then served on the faculty of the college from July 1947 to June 1950.[3]