Max Lukenbach was born on August 15, 1932, in Letts, Iowa. After attending Iowa State Teacher's College and the University of Arizona, he enlisted in the U.S. Naval Reserve on October 4, 1953, and entered the Aviation Cadet Program of the U.S. Navy on February 21, 1954. Lukenbach was commissioned an Ensign and was designated a Naval Aviator on August 11, 1955, and then completed A3D Skywarrior training before serving with VAH-2 at NAS Whidbey Island, Washington, at NAS North Island, California, and back to NAS Whidbey Island from November 1955 to August 1959. His next assignment was as as an A3D and F4D Skyray pilot at NAS Jacksonville, Florida, from September 1959 to August 1961, followed by U.S. Naval Postgraduate School in Monterey, California, from August 1961 to August 1963. After completing RA-5C Vigilante Replacement Air Group training, LCDR Lukenbach served with RVAH-13 at NAS Sanford, Florida, until November 1965, when he deployed with the unit aboard the aircraft carrier USS Kitty Hawk (CV-63). He was killed in action on December 22, 1965, while flying a mission over North Vietnam, but was officially listed as Missing in Action until declared dead on May 19, 1969, during which time he was promoted to the rank of Commander. His remains have never been returned.

His Distinguished Flying Cross Citation reads:

For heroism and extraordinary achievement in aerial flight on 22 December 1965 as pilot of a jet aircraft, serving with Reconnaissance Attack Squadron THIRTEEN, embarked in USS KITTY HAWK (CVA-63) during a combat mission over hostile territory in North Vietnam. Commander (then Lieutenant Commander) Luckenbach was participating in a mission with the assignment of obtaining post-strike photography of a railway bridge, a highway bridge, and a strategic power plant in a very heavily-defended area. Last observed while proceeding toward his objectives in the face of unfavorable weather conditions and intense enemy antiaircraft and missile defenses, Commander Luckenbach, by his courageous and selfless devotion to duty, upheld the highest traditions of the United States Naval Service.