George; these lyrics exactly mimic the first two verses of this song as recorded by Capecaille; so yes, I am guessing it is the same song. I do not know if the tune they used was traditional for these lyrics; it does not really sound like a lullaby to me, as they recorded it; too sad and the rhythm is not very regular...

It also seems to me I have seen more than one song with that lyric and title, dean cadalach samhach; so maybe there's more than one?