I guess sometimes it is a matter of finding the right key words. The tune is under Billy Byrne of Ballymanus in JC Tunefinder and the following information and tune in abc is given in Ceolas.



BILLY BYRNE OF BALLYMANUS. AKA and see "Billy Byrne's Lament," "Ormonde's Lament," "The County of Mayo," "A Lament for Thomas Flavell." Irish, Air or March Tune (2/4 time). C Major (Joyce/1909, Roche): D Major (Joyce/1890, O'Neill). Standard. One part. "This rude ballad is one of a class which were very common all over Ireland for half a century or so after the rebellion of Ninety-eight. I give it partly from memory, partly from a printed ballad-sheet in my possession, and partly from the copy published 40 years ago by Father C.P. Meehan in his book 'The O'Tooles'. He took his copy from a MS. written by a schoolmaster named MacCabe of Glenmalure. There are other verses in which the informers' names are given in detail, but they are as well omitted here. 'Billy Byrne of Ballymanus' (near Rathdrum, and nearer to Greenan in Glenmalure, county Wicklow) was an influential and very popular gentleman of the County Wicklow who was convicted and hanged on the evidence of informers after the rebellion. Father Meehan gives an account of him in the above-mentioned book. The tune is well known and extremely popular in the south-eastern counties; and I think not without good reason, for it appears to me a very beautiful melody and most characteristically Irish. I printed it for the first time in 1872 in my Ancient Irish Music. I have often heard it played by itinerant musicians in the streets of Dublin. It was sometimes used as a march tune" (Joyce). In his 1873 work Joyce states the tune was extremely popular in the counties of Dublin, Wicklow, Wexford and Carlow, and gives the Leinster setting.
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Cazden (et al, 1982) found the tune in tradition among ballad singers in the Catskill Mountains of New York, and prints it for the song "Wild Americay." He finds, in addition to being a popular tune for Irish ballads and songs, it has been found in the Northeast-Maritimes region (particularly in lumbercamp repertory), and notes that Ron Edwards reports two songs from Australia sung to a similar melodies. O'Neill (1913) records the melody being used for songs entitled "A Lament for Thomas Flavell" and "The County of Mayo." See note for "The Enniskillen Dragoons" for brief discussion of structure and other tunes in this class. O'Neill found (printed in Alfred Perceval Graves' Irish Song Book) an old song called "The County of Mayo" sung to the "Billy" tune, commencing "On the deck of Patrick Lynch's boat I sit in woeful plight." Joyce (Ancient Irish Music), 1890; No. 86, pg. 88. Joyce (Old Irish Folk Music and Song), 1909; No. 374, pg. 179 (with lyrics). O'Neill (1850), 1979; No. 117, pg. 21. Roche Collection, 1982; Vol. 3, No. 48, pg. 13.