Sir William Lindsay Murphy was born on 4 May 1887, in Ballinglough, Roscommon, Ireland, the son of Canon R.W. Murphy. He was educated at the Abbey, Tipperary, and at Trinity College, Dublin, where he was a classical scholar and a Gold Medallist. He entered the Ceylon (Sri Lanka) Civil Service in 1910, rising to the rank of Principal Assistant Colonial Secretary, 1928, and Chairman, Municipal Council, and Mayor of Colombo, 1932-1937. He was posted to Bermuda as Colonial Secretary, 1942-1945, and served as Acting Governor in 1943. He became Governor and Commander-in-Chief of the Bahamas, 1945-1949. He retired briefly in 1949 and emigrated to Rhodesia (Zambia and Zimbabwe) with his family and took up farming. He was Director of Rhodesian Selection Trust Ltd., Mufulira Copper Mines Ltd., and other companies in the same group from 1953. He was called out of retirement to serve as Acting Governor of Southern Rhodesia (Zimbabwe), 1954, and Acting Governor of Southern Rhodesia (Zimbabwe) and Acting Governor-General and Commander-in-Chief, Rhodesia and Nyasaland (Zambia, Zimbabwe, and Malawi), 1957. He became briefly involved in politics in 1958, when, on the formation of the United Rhodesia's Party under the chairmanship of Garfield Todd, he was elected its President.

Murphy received a CMG (Companion of the Order of St Michael and St George) in 1944, and the KCMG (Knight Commander of the Order of St Michael and St George) in 1946. He was also a Knight of the Order of St John.

In 1922, Murphy married Elizabeth Mary 'Betty' Ormsby (daughter of Col. the Rev. T. Ormsby of Co. Galway) with whom he had three sons and two daughters. Mrs (later Lady) Murphy took an active interest in the social services and also in the Red Cross in the countries in which her husband served, and she received the MBE (Member of the Order of the British Empire) in 1935 for her work in this field in Ceylon (Sri Lanka). Later on, she became President of the Bahamas branch of the Red Cross. In Rhodesia (Zimbabwe), the Murphys set up a school for the children of the African workers on their farm. After Sir William's death in 1965, Lady Murphy continued to take an interest in education and helped to support many children at various schools in Rhodesia (Zimbabwe).