The contract to build Lapon was awarded to Newport News Shipbuilding and Dry Dock Company in Newport News, Virginia, on 24 October 1963 and her keel was laid down there on 26 July 1965. She was launched on 16 December 1966, sponsored by Mrs. Charles D. Griffin, wife of Admiral Charles D. Griffin (1906–1996), and commissioned on 14 December 1967, with Commander Chester M. "Whitey" Mack in command.