Like his older brothers, Lindsay was educated at Harrow School. He played for the schoolcricket team for three years, captaining it in 1928, his final year, when he averaged 55 runs per innings. also representing a combined Public Schools side. He went on to Balliol College, Oxford, and began playing for the Oxford University Cricket Club, making his first-class debut in June 1929, against Gloucestershire. A wicket-keeper and right-handed top-order batsman, Lindsay went on to play three more first-class games during the 1929 season – two for Oxford, and one for Scotland, his father's place of residence. His sole appearance for Scotland came against the touring South African team, which was completed within two days as Scotland lost by an innings. Lindsay played only once at first-class level during the 1930 season, but the following year made five first-class appearances for Oxford, including in the annual University Match against Cambridge University. He also made two County Championship appearances for Kent, against Warwickshire and Middlesex within the space of five days. He kept wicket and opened the batting against Warwickshire, but Les Ames, the county's usual wicket-keeper, returned against Middlesex, with Lindsay playing solely as a batsman. In 1932, Lindsay played in another five first-class fixtures for the university, and against Lancashire scored 63 runs, his first and only half-century. His season included matches against two touring international teams, the Indians and the South Americans, with his game against the South American composite side being his final first-class match.
Professional career and later life
In 1932, Lindsay joined the Sudan Political Service, which administered Anglo-Egyptian Sudan. During the Second World War, he was twice given an emergency commission as a second lieutenant in the Sudan Defence Force. Towards the war's end, in 1944, Lindsay transferred to the legal department of the civil service. He was appointed to the country's judiciary, as chief justice in 1950 according to one source and 1954 according to another source. He served until 1955, as one of the last British chief justices before the country was given independence in 1956. Upon leaving office, he was made a Knight Commander of the Order of the British Empire in the 1955 Birthday Honours. After retiring, Lindsay opened a law firm in Nairobi, Kenya, where he lived until his death in 1975. He had married three times – firstly in 1937, to Sevilla Glass Hooper; secondly in 1962, to Elizabeth Doreen Sturman; and thirdly in 1975, to Michaela Denis.