Musica Britannica vol XV (Music in Scotland 1500-1700, ed. Kenneth Elliott) has the original tune, plus bass, for "I come from Hevin [hecht] to tell".
The notes add that, during the eighteenth century, the song was often sung to Lady Bothwell's Lament. I don't know if this is what I know as Lady Anne Bothwell's Lament("Baloo my boy, lie still and sleep / It grieves me sair to hear thee weep"), which looks decidedly eighteenth century to me. Anyway, it fits the Luther/Wedderburn poem quite neatly; I usually just do the two 'Balulalow' verses, 13 & 14, not the whole thing.