Lyons received his PhD in 1970 at the University of Chicago under John Griggs Thompson with a thesis entitled Characterizations of Some Finite Simple Groups with Small 2-Rank. From 1972 to 2017 he was a professor at Rutgers University.
With Daniel Gorenstein and Ronald Solomon he wrote, and is continuing to write, a series on the classification program for finite simple groups, a program in which the three of them were major participants. Nine volumes of this series have been published so far. He discovered a sporadic group which Charles Sims constructed and called the Lyons group Ly.
In 2012 he shared the Leroy P. Steele Prize for Mathematical Exposition, awarded by the American Mathematical Society, with Michael Aschbacher, Stephen D. Smith, and Ronald Solomon. In 2013 he became a fellow of the American Mathematical Society "for contributions to the classification of the finite simple groups, including the discovery of one of the 26 sporadic finite simple groups.".