My family were Lallys from Loughrea, Kiltullagh, Ballymacward. I often come across other Lallys from this area but cannot prove they were related. Except that the University of Leicester has done research on relationships between people with the same surname. On average two men with the same surname have a 24% chance of being related. Names relating to an occupation, such as Baker, have a lower probabilty as there were bakers in every town. What raises this probablity is if the name is rare, has an unusual spelling, if it relates to a specific locality, there was a history of no geographic movement. I would claim that Lally falls into these categories. Also the name Lally relates to a specific, fairly small and local, tribe. In such a case the probablity of two men being related rises to 93%, they say. So I think all the Galway and Mayo Lallys in the 1830s were related. This is the basis on which I wrote my book about three Lally families, including some Marys, in the Great Famine, "The Leaving of Loughrea" and I hope you don't mind the advertising as we are all family. Please have a look at it on google or amazon. Thanks