Lily of the West (http://www.contemplator.com/folk2/lilywest.html). On my pages the tunes to Lakes and Lily are noticably similar, but when someone wrote me they were the exact same tune I confess I can't hear that much similarity!
Rev. S. Baring-Gould collected versions of Lily of the West in Devonshire, Yorkshire and elsewhere. Baring-Gould felt the ballad was of definite Irish origin (though it may not have been sung to a similar air) and traced it back to at least 1839. The lyrics in Sam Henry's Songs of the People are an Irish version which begins; "When first I came to Ireland..."
Another theory of it's origin traces it back to the West of Ireland during the time of Cromwell.