Lady Fairlie and the Earl of Hexham appear to be fictional titles.
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Lillie Langtry (1853-1929) was born Emilie Charlotte Le Breton on the island of Jersey. She married the Irish landowner Edward Langtry in 1874, and was the mistress of the Prince of Wales (later King Edward VII) between 1877 and 1880. In 1879, she also started affairs with the Earl of Shrewsbury and Prince Louis of Battenberg. In 1881 she made her acting debut in an amateur production in London, and went on to develop a career as an actress and vaudeville performer in Britain and the United States.