Lewis was a "student" (that is, fellow) of Christ Church, Oxford and Professor of Ancient History at the University of Oxford. In his obituary in The Guardian newspaper (16 July 1994), it was stated that Prof. Lewis "has been, for the last two or three decades, the world's leading authority in the field of Greek epigraphy." He was also an authority in several ancillary fields, "a profoundly learned scholar in Greek history" according to the Princeton Alumni Weekly memorial tribute.
A native of London, he attended the City of London School, was an undergraduate at Corpus Christi College, Oxford (where he said he was one of the last people to be allowed to do postgraduate work without registering for a higher degree) and studied for his PhD in classics at Princeton University. He also studied at the Institute for Advanced Study in Princeton, New Jersey, the British School in Athens, and at Christ Church, Oxford.
Lewis was a scholar of ancient Greek history. Much of his work was concerned with inscriptions, but he insisted (in particular in an address to the epigraphic conference in University of Cambridge in 1967) that epigraphy should not be an activity for initiates only, but should be one means among others to the end of understanding the ancient world as fully as possible. He took a particular interest in what could be learnt from texts which even those who venture into the world of inscriptions find intimidating, accounts of expenditure and inventories of temple treasures; and this interest was extended to oriental documents, in particular the fortification tablets from Persepolis.
His Jewish faith prompted the development of a second area of expertise, Middle Eastern history.
Lewis was very proud of his work in editing three volumes on Archaic and Classical Greek history in the second edition of the Cambridge Ancient History. He published a book, Sparta and Persia, in 1977, and a shorter work, The Jews of Oxford, in 1992. He also edited several Oxford publications in the classics, including The Decrees of the Greek States published posthumously in 1997. He also published hundreds of book reviews, as many as eighteen appearing in a single year (1977).