Is the Elizabethan Virginal Book the music-book Lover was likely referring to? Here is a book which analyzes this book: An Elizabethan Virginal Book : Being a Critical Essay on the Contents of a Manuscript in the Fitzwilliam Museum at Cambridge:
An Elizabethan Virginal Book by Edward Woodall Naylor, 1867-1934
On pages seven and eight it says:
The [musical] connection of England with Ireland is marked by the titles of three pieces in the Fitzwilliam Book:—
(a) The Irish Dumpe, ii. 236. Anon.
(b) The Irish Ho-Hoane (Ochone), i. 87. Anon.
(c) Callino Casturame, ii. 186. Arranged by Byrd.
(Corruption of "Colleen oge asthore.")
The last of these is referred to in Shakespeare, "Henry V." iv. 4, l. 4, where it is spelt "Callino, Castore me!"
The second of these Irish tunes, the Ho-Hoane, is a very first-class example of real pathos, and should be heard. It will be found a true expression of tender sorrow. To me the piece is a wonder, for I believe it to be about 400 years old.
The first, the Irish Dumpe, ii. 236, is a cheerful tune, by no means like the English Dump, which (according to Shakespeare himself in Lucrece, line 1127) was a doleful ditty, hence the "doleful dumps," ...
More information on the subject at "Our Musical Page" in The Celtic Monthly: A Magazine for Highlanders, Volume 4:
Here it is stated that "Irish songs and dance tunes were all the fashion at Court at one period of Elizabeth's reign." And if I understand correctly, it is suggested that "Callino casturame" might have a Scottish rather than Irish origin.
And in Chambers's Edinburgh Journal, Volume 9, the question of why such a fuss is made over the national origin of a particular air is pondered: