Born in Briton Ferry, Neath in Wales, Lindsey was the younger brother of racing driver Roy Eccles and the brother-in-law of Marjorie Eccles who also used to race. Lindsey was a director and later the managing director of the Briton Ferry Steel Company.
He drove Bugatti's with great enthusiasm and owned or raced Types 37, 39, 35, 51, 57 and 59. He raced his T35 and T51 at Brooklands and Donnington Park, with his best result a 2nd place in the 1933 Donnington Park Trophy. In 1935 he bought a new T59.
Lindsey died in Sketty, Swansea on August 29 1991.