Naismith was born to John Naismith, who worked in the car tyre trade, and Mary Francis (née Redmond) Naismith, a well-known clairvoyant. Her sisters Jill and Sheila were also actresses. Naismith trained at the Italia Conti Academy of Theatre Arts.
In 1928 she appeared in her first film, The Bravo, produced by the Welsh Person Elder Company and based on a novel by W. W. Jacobs, who was involved in the production. The lead role of Lucy was selected from fifty auditioned actresses, with Jacobs reportedly impressed by Naismith's performance. Her social circle widened considerably through her association with actor and later Member of Parliament Derwent Hall Caine, whose connections brought her into contact with Ishbel MacDonald, who served as hostess to her father, Prime Minister Ramsay MacDonald. Press reports in 1929 indicated an engagement between Naismith and Hall Caine, though this was subsequently retracted.
Naismith also took part in a significant moment in broadcasting history: a live image of her was used by John Logie Baird to demonstrate his all-electronic colour television system, Telechrome. She had a strong personal interest in mechanical pursuits more broadly — in the same period she was competing in a concours d'élégance with her own car, and she later held a pilot's licence, participating in the King's Cup Air Race in 1938 as a passenger aboard a BA 4 plane piloted by T.W. Morton. Press coverage from the period described her as "the female racing driver and formerly chauffeur to Mr Ramsay MacDonald."
Naismith's introduction to competitive motorsport came through rallying, where she frequently drove Standard cars. She entered the RAC Rally in both 1932 and 1933.
Her circuit racing took place at Brooklands between 1931 and 1934, most often in a supercharged Salmson belonging to Derwent Hall-Caine. Her first appearance at the track was in the 1931 "Society Ladies' Private Handicap," an event organised by Barbara Cartland primarily for the benefit of a film crew, in which all entrants drove MGs. From that starting point she moved into genuine competition. In 1933 she won a Ladies' Handicap against nine other competitors, among them Fay Taylour and Elsie Wisdom — two of the most accomplished women racers of the era — a result that demonstrated she could hold her own in substantive company.
In 1934 she entered two further Brooklands events: the BARC First Long Handicap in July and the First Kingston Junior Long Handicap in October, finishing third in both races. The October event proved to be her last race at the circuit; she was fined on that occasion for exceeding the track limits.
In 1934 Naismith was photographed by the Bassano studio, and the portrait is held by the National Portrait Gallery in London. She married RAF officer John Towers Mynors in 1941. She died in London on 28 November 1963, aged 60.