He was regarded as a prodigy, especially in mathematics, and Robert Smith, master of Trinity College, took him under his wing and paid for his attendance.
Due to his Ashkenazi Jewish origins, Lyons was not permitted to become an official member of the University of Cambridge.
Nevertheless, his brilliance resulted in his publication Treatise on Fluxions at the age of 19, and his enthusiasm for botany resulted in a published survey of Cambridge flora a few years later.
Later, Banks secured Lyons a position as the astronomer for the 1773 North Pole voyage led by Constantine Phipps.
There he died of measles on 1 May 1775, at the age of only 36, while preparing a complete edition of Edmond Halley's works sponsored by the Royal Society.