Alice Lalor's parents were Denis (d 1799) and Catherine Lalor, originally of Queens County, but later of Ballyragget, Co Kilkenny. You will find him on the Oaths oa Allegiance at Abblyragget in 1775. The biogragy of Joseph M Doran (also online at www.archive.org) of Philadelphia names his parents as Mary Lalor and Michael Doran, who arrived in Philadelphia in 1795. Another of Mary's cousins was the famous Patt Lalor MP of Tenakill and the General Joseph O'lawlor of Granada, Spain. I am still working thought the links.
Reviewing the Trenton genealogy, I rhink everything from 'John Lalor of New York married (1) Anderson (2) Annastasia Dwyer' down is correct and everything in Ireland is incorrect. A Jeremiah Lalor left a will in Ballyragget in 1753 (he died aged 46), and I suspect he is a more likely cancidte to be the father of John of new York and uncle of Denis.
John