In 1657, William Lucy published an attack on the philosophy of Thomas Hobbes, and in particular on Leviathan (1651), using the pseudonym William Pyke, Christophilus, and circulated by Humphrey Robinson.
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On 17 March 1661, Halton wrote to Joseph Williamson that he had offers of chaplaincies from William Lucy, bishop of St. David's, and from Elisabeth of Bohemia.
He had two brothers, John Neville, Baron Neville (c.1410-1461), who was slain at the Battle of Towton on 29 March 1461, and Sir Thomas Neville (died c. 1461) of Brancepeth, Durham, and one sister, Margaret, who married Sir William Lucy of Woodcroft, Bedfordshire.
He was a first generation Barbadian born in England and second son of Abel Hendy Jones Greenidge (who came up to study and remained at Oxford as an academic) and his wife Edith Elizabeth, the youngest daughter of William Lucy, at that time the sole owner of Lucy Ironworks, previously known as the Eagle Ironworks, in Walton Well Road, Jericho, Oxford.