This is Child's number #208, but is often confused with the entirely different song (though it deals with the same subject) Derwentwater's Farewell, which is in the DT (and wrongly given the Child number). Child (English and Scottish Popular Ballads) has nine texts, from Northern England and from Scotland.There is an entry at The Traditional Ballad Index:
Roy Palmer (Bushes and Briars: Folk Songs Collected by Ralph Vaughan Williams, 1983/99) comments:
"The Derwentwater family had estates in Cumberland and Northumberland. The family seat, originally on an island in Derwentwater (hence the name) was abandoned in the 17th century in favour of Dilston Hall, near Corbridge. James Ratcliffe, the third Lord Derwentwater, and the subject of the ballad, seems to have been genuinely loved by his family, servants and tenants. When he was beheaded in 1716, for his part in the abortive Jacobite rising of the previous year, he was widely mourned..."
Child, of course, gives far more detailed historical information. The song has also been found ( in both England and Scotland) as Lord Dunwaters, Lord Allenwater, Lord Arnwaters and Lord Ellenwater; some texts were given in the Journal of the Folk Song Society (No. 13, 1909), but I don't have those -yet!-, so can't help further just now; there are, I think, additional examples in Bronson's Traditional Tunes of the Child Ballads, but again I don't have the relevant volume. I assume you have the Lord Ellenwater set that Vaughan Williams got from (presumably) Cambridgeshire, and which appeared in the Palmer collection?