I asked Gaelic speaker Bill Maguire of the Memphis Dulcimer Festival what he thought. He did note that Grian Sliabh (pronounced Green Sleeve) may indeed be a couple of Irish words. Grian = sun, and sliabh = mountain. As far as the Henry VIII connection, I believe he may have maintained a couple Irish harpers at his court. If he's responsible for the absolutely dreadful lyrics in English, one may speculate that he put them to a perfectly decent Irish tune! He is also supposed to have compared Ireland to an Irish harp, something in regard to the difficulty of keeping the country in tune, but you'll need to contact a more compleat scholar than me for an exact quote!