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Lacey was born on 28 September 1935 in Harrow, London, England. He studied at the Harrow Weald Grammar School and at the London Academy of Music and Dramatic Art. Lacey was married to Mela White from 1959 until they divorced in 1971. Then he was married to Joanna Baker from 1972 until they divorced in 1991. He had three children. Lacey died on 15 May 1991 from liver failure cause by his liver cancer in London, England, aged 55.