In the Wikipedia article on James Cotter the Younger, it is actually a book by A. Marshall that is the source for the statement, that the wife of the Lord Lieutenant of Ireland at the time of the trial is the granddaughter of John Lisle, but it doesn't actually name these people.
I'm not sure when the trial actually happened but Charles Paulet, 2nd Duke of Bolton, was Lord Lieutenant from April 1717 to Nov 1719 and he was followed by Charles Fitzroy, 2nd Duke of Grafton from 1720-1724. There might have been a gap of some months between one and the other?
However I can't see that the wife of Charles Fitzroy was a granddaughter of John Lisle either. She ws Henrietta Somerset, daughter of Charles Somerset, Marquess of Worcester and Rebecca, the daughter of Sir Josiah Child. There also doesn't seem to be enough time for a granddaughter of John Lisle to be of marriageable age by 1719-1720?
I think that maybe Mr or Ms Marshall is either mistaken or has been misread?