Found a bit more at the Library of Congress website:
An index to the vocal works of Thomas Augustine Arne and Michael Arne, by John A. Parkinson.Arne, Thomas Augustine, -- 1710-1778 and Arne, Michael, -- 1741?-1786. So Michael Arne the composer could have been his son, but not his father, born when Thomas was about 31. Numerous places now, I am finding, of Michael being the composer of "the lass" song. Still others, as in my printed music, T. Arne. From the catalog of works by Michael, it seems to fit with his other works more than those of Thomas.

Alice