Lukoff was born in Philadelphia, Pennsylvania to Aaron and Anna (Slemovitz) Lukoff. He graduated from the Moore School of Electrical Engineering at the University of Pennsylvania in 1943. While at the Moore School, he helped develop the ENIAC and EDVAC computers. He followed ENIAC co-inventors J. Presper Eckert and John W. Mauchly to their newly formed Electronic Control Company, which became Eckert-Mauchly Computer Corporation, then became part of Remington Rand in 1950 and Sperry Corporation in 1955. Lukoff assisted Eckert and Mauchly with the development of the UNIVAC computer. He stayed with the company until his death.
Lukoff died of leukemia on September 24, 1979. At the time of his death, he lived in Fort Washington, Pennsylvania. He was survived by his wife, Shirley Rosner Lukoff; his three sons, Arthur, Barry, and Andrew; and his daughter, Carol.
Lukoff's memoir, From Dits to Bits, details his experiences as a first-hand observer of the birth of the computer industry.