My grandmother, Sara Rosina Moriarty Griffith, who died in 1945, always told her children and grandchildren that she was the cousin of John L. Sullivan the boxer. Her parents were Simon Lawson or Louis Moriarty and Emily Philomine Picquette. Simon was from County Kerry, Ireland. I don't know when he came to the U.S. or anything else about him. I think they lived in Iowa for awhile.
Does any of this tie in with your research? Any Moriarty info you could send would really be appreciated!!