Hi - Just starting the research of my fathers family. As has been told to me, my great grandfather, David Martin Lally (O'Mullally) came to the US during the famine, and married Jennie Jenks, possibly from northern Ireland. They married in Oswego, NY (or Fulton, Red Creek, Dexterville), in the later 1800s. They had 4 children: Thomas, who died in infancy, George Thomas Lally (my grandfather), Mary Ann, and Bernadette. My grandfather, George, moved to Rochester, NY and raised his family there.
Some familiar/related names are Feeney and Cullinan.