The son of a British diplomat, L'estrange was born in Lytham St Annes in 1934 and was educated at Blackrock College, Dublin; the University of Chicago; and the Sorbonne in Paris. He undertook National Service, being deployed as part of the Parachute Regiment in Suez during the 1956 crisis. He was commissioned, reaching the rank of lieutenant colonel before returning to Ireland to study modern history and political science at the University of Dublin.