The Lawrence family are first recorded in east Galway in the late 16th century. A John Lawrence married a daughter of one of the O'Maddens and later acquired property at Ballymore. The Lawrence family were dispossessed of this property under the Cromwellians but were later granted Belview or Lissareaghan in 1677. In 1851 Walter Lawrence advertised for sale in the Encumbered Estates' Court approximately 4000 acres in the baronies of Dunmore, Clare and Longford, county Galway and 311 acres in the parish of Shrule, barony of Kilmaine, county Mayo. Patrick Nolan purchased Lawrencetown and substantial portions of the estate in the Milltown area but sale of other lots were adjourned and some of the lands were not sold until 1852. Dominick O'Flaherty bought the Shrule portion. The Lawrences still owned about 2000 acres in county Galway in the 1870s and occupied the mansion into the twentieth century. By the 1920s most of the land had been sold to the tenants and the house was demolished.
See http://www.lawrencetown.com/lawrences.htm for more on the Lawrences. Also see http://www.askaboutireland.ie/reading-room/history-heritage/big-houses-of-ireland/lawrence-family-album/index.xml