Lindsay was commissioned lieutenant on 20 August 1759.
He was present at the inconclusive Battle of Porto Praya on 16 April 1781 and was promoted commander with seniority from 22 April upon his appointment by Commodore George Johnstone to the Porto 12, which had previously been the French sloop Arlequin, and in which he returned home with despatches.
In August 1783 Lindsay joined the Scout 16, which vessel was paid off in 1786.
During the Spanish Armament of 1790 he commanded the Roebuck 44 as a hospital ship in the Grand Fleet, and he retained her until she was paid off at the end of the Russian Armament in September 1791, during which time he was posted captain on 21 September 1790.
Lindsay did not see any further service, and he died in 1798.