Lennard-Jones was born at Leigh in Lancashire, the son of a retail furnisher, was educated at Manchester University and, after service in the Royal Flying Corps, at Cambridge University, where he obtained his PhD in 1924. He moved to Bristol University in 1925, serving as professor of theoretical physics from 1927 until 1932 when he returned to Cambridge as professor of theoretical chemistry. He resigned in 1952, shortly before his death, to become principal of the University of Keele.

Lennard-Jones began his research career in the early 1920s by attempting to produce a formula from which interatomic forces could be calculated. He later moved into the field of theoretical chemistry, doing much to promote the molecular-orbital theory of Robert Mulliken.