Lindsay was born in Goolwa, South Australia, a son of Captain John Scott Lindsay (ca.1819 – 29 June 1878), master mariner formerly of Dundee, Scotland, and his wife Catherine, née Reid (ca.1822 – 28 May 1884). John Lindsay commanded the brig Europa and Sir James Fergusson's yacht Edith before a career on Murray River steamers which included a pioneering trip to Brewarrina with W. R. Randell in 1859.
