I thought it pretty much settled that the melody for Lay Down Your Weary Tune was a variant of "The Water is Wide" or "Waly, Waly". There are several hymns in the Methodist Hymnal using a similar melody. Two that come to mind are "When Love Is Found" and "Gifts of Love" but neither is all that old. There is another hymn "When I Speak", but I think it also of rather recent vintage. All at least less than a century in age as far as the words are concerned. The melody is also sometimes used for "When I Survey the Wondrous Cross".