"Ane Compendious Buik of Godly and Spirituall Sangis..." 1567, was written by the brothers James, John and Robert Wedderburn.

The poem "I Come from Heuin to Tell," is a translation of the Christmas Eve Carol which Luther wrote for his son, Hans, "Vom Himmel hoch," first published in 'Geistliche Lieder," 1535.
Luther's tune is in "Songs of Praise," No. 365. Note on p. 395, "The Oxford Book of Carols," Percy Dearmer, R. Vaughan Williams and Martin Shaw, Sixteenth Impression, 1947 (There are newer editions and pagination and content may be different).
The Oxford Book of Carols has the music for "Balulalow' in an arrangement by Peter Warlock, arranged for soprano solo, with only two verses:

O my dear heart, young Jesus sweet,
Prepare thy cradle in my spreit,
And I sall rock thee in my heart,
And never mair from thee depart.

But I shall praise thee evermore,
With sangis sweet unto thy gloir;
The knees of my heart sall I bow,
And sing that richt 'Balulalow.'


stonejohn mentions hearing two tunes. One may be 'Balulalow.' the other Luther's.