Lyons went 12-of-17 from the field, including a trio of 3-pointers, and the Wildcats (27-7) went 9-of-15 from long range overall en route to their second Sweet 16 appearance in three seasons.
Solomon Hill added 13 points and 10 rebounds for Arizona, which built a 30-9 lead in the first half and never looked back.
The Wildcats advance to play the winner of Sunday's game between No. 10 Iowa State and No. 2 Ohio State in the West Region semifinals.
Fourteenth-seeded Harvard (20-10) was seeking a Cinderella run in the NCAA Tournament but the Crimson's hopes were dashed by poor shooting -- they managed to connect on only 27.6 percent from their tries from the field.
Kenyatta Smith led Harvard with 10 points.