There are 23 Lawleys in the 1901 Ireland census, most of them from Counties Cork and Wicklow.
There are no death records for a Walter Lawley or a Bridget Lawley in Ireland up to 1900, but they may have both died before civil death recording became commonplace in the 1860s, or Bridget may have remarried. Or they may have emigrated themselves. Or they may be recorded as Lawler, Lowley, etc.
Unless you're very lucky and they were recorded in parish church records, this might be a brick wall.