A William Greene (1770?) may have been the father of Luke (also Thomas, Patrick, Mary and William):

Luke Greene (1798 - 1885) Ballycotton Co. Clare (m. Ann Healy (1810?) Ennistimon)
Chn: Michael Green (1833- 1904) Ballycotton to Australia (m. Ellen Murphy)	William Green (1840?) Ballycotton Co.Clare	Siblings Thomas and Ann went to Australia with Michael
	Chn of William:
Austin Greene Co. Clare	William Greene (photo) (1870-?) Liscannor Co. Clare m. ?Kelly Buried St. Bridget's Well
	William Greene (1895-1972) Liscannor Co. Clare m. Anne MacNamara
	Patrick Greene (1925) Carrowduff Michael Greene London Jo Greene Birmingham William Greene Birmingham Mary Greene USA Nancy Greene UK