He was the fifth son of Colonel the Honourable George Napier, and his second wife, Lady Sarah Lennox, seventh daughter of the 2nd Duke of Richmond, and one of the famed Lennox sisters.
The Lennox sisters were the daughters of Charles Lennox, 2nd Duke of Richmond in the Peerage of England and 2nd Duke of Lennox in the Peerage of Scotland, and Lady Sarah Cadogan (1705–1751), daughter of William Cadogan, 1st Earl Cadogan.
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As a young woman, she fell ill with a wasting disease--possibly tuberculosis--and her older siblings sent her first to Kingsgate and then to France in a vain effort to recover her strength.
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Georgiana Carolina Fox, 1st Baroness Holland, of Holland (27 March 1723 – 24 July 1774), known as Lady Caroline Lennox before 1744 and as Lady Caroline Fox from 1744 to 1762, was the eldest of the Lennox Sisters, immortalised in Stella Tillyard's book Aristocrats, and the television series based on it.
Lady Sarah Cadogan, daughter of the first Earl of the first creation, married Charles Lennox, 2nd Duke of Richmond, and was the mother of the famous Lennox sisters (and also the grandmother of Charles James Fox).