Naismith was born as Lawrence Johnson in Thames Ditton, Surrey, in 1908. He attended All Saints Choir School, Margaret Street, London and was a chorus member for a 1927 production of the George Gershwin musical Oh, Kay!. He later worked in repertory theatre and ran a repertory company of his own. At the outbreak of the Second World War he joined the British Army where he became an officer in the Royal Artillery.
His film roles included Carrington VC (1954), Richard III (1955), A Night to Remember (1958), Sink the Bismarck! (1960), The World of Suzie Wong (1960, Jason and the Argonauts (1963). He played the non-singing role of Merlin in the 1967 film version of the musical Camelot and appeared in the James Bond film Diamonds Are Forever (1971) as the chairman of the Diamond trading syndicate.
He appeared on Broadway in the Meredith Willson musical Here's Love in 1963, opposite Janis Paige.
In 1965, Naismith played the title role of the Virginia statesman George Mason in the NBC documentary series, Profiles in Courage. william Bakewell played George Wythe in the episode, and Arthur Franz was cast as James Madison. In 1965, Naismith guest-starred as barber Gilly Bright in episode 25, "The Threat" of the ABC military drama, 12 O-Clock High (TV series) and in the ABC action drama, The Fugitive, starring David Janssen. In 1969 he played Don Q Hought in an episode of Bonanza. He played Judge Fulton in the television series The Persuaders! (1971), with Tony Curtis and Roger Moore. He portrayed Emperor of Austria Franz Joseph in the BBC production Fall of Eagles (1974). Naismith played the Prince of Verona in the BBC Television Shakespeare version of Romeo and Juliet. He also appeared in the BBC sitcom Oh Father (1972).