Lindsay was born in Boston, Lincolnshire, and emigrated to South Australia on the HMS Buffalo arriving in December 1836 in company with Governor Hindmarsh, James Hurtle Fisher (the Resident Commissioner), Osmond Gilles (Treasurer), and the Review C. B. Howard (Colonial Chaplain), and was present at the proclamation of the province under the historic gum tree at Glenelg.
In July 1839 they transferred ownership of the land to A. F. Lindsay and George Milner Stephen. then took up a farm in the Encounter Bay district. He was succeeded by (the unrelated) John Lindsay, then served the same electorate April 1870 – December 1871, with Emil Wentzell. And September 1873 – April 1878, with William Rogers and James Boucaut.
He argued strongly for the construction of light railways on the narrow gauge system, but received little support, though he was later largely vindicated.
Lindsay married Charlotte Henrietta Leworthy (c 1823 – 6 February 1915) on 20 July 1852. They had a farm "Edyell" in Victor Harbor.
Their children included:
Beatrice Mary Charlotte Lindsay (27 May 1853 – 28 November 1949) married William Hope Ross ( – 27 April 1929) on 29 April 1874
Helen Georgina Fydell Lindsay ( – 2 June 1925) married Aubrey Percival Gwynne (c 1860 – c 30 May 1930) on 21 April 1896. Betana Caroline Lindsay (22 September 1861 – 30 April 1943) married Edgar J Salom (c 1873 – 6 July 1898).
She ran a rest home in North Adelaide.
Gertrude Theodora Fydell Lindsay ( – 1 April 1946) married Doctor Robert Walter Stewart (c 1849 – 11 November 1921)
Clarice M. Amelia Fydell Lindsay ( – 25 June 1941) married Horace James Page (1856 – December 1936) on 22 December 1915
He was convicted for assaulting John Hindmarsh (son of Governor Hindmarsh) in November 1860. He was not related to John Lindsay, who followed him as a representative for Encounter Bay.
Lindsay served as the first member of the House of Assembly for the single-person electorate of Encounter Bay for the terms March 1857 – April 1860, when his colleagues were Benjamin Herschel Babbage and Henry Strangways. Gwynne was a member of the 1891 Royal Geographical Society "Elder Expedition" to Central Australia under David Lindsay (not closely related) He died a virtual recluse. Arthur Reginald Fydell Lindsay (30 November 1863 – 27 September 1913) was member of SAJC and American Red Cross.
