Douglas Hyde's Abhráin Diadha Cúige Connacht / The Religious Songs of Connacht, volume I, pp. 130 - 137, is the reference work from which I will open this thread. That said:

This particular sean-nós has an elevated status within traditional Irish song. True, for listeners outside of this genre, it may be all but unknown. But within the outer circle, if you will, this lyric has gotten a great deal of attention. The song is in more than one published collection; at least one doctoral dissertation (Angela Bourke a/k/a/ Angela Partridge) has been published with the Gaelic song as its title, as well as its subject; several generations of Irish musicians have now recorded performances of the song. In short, a strong argument can be made for giving this song a thread of its own.

It is also a fact that "Caoineadh na Tri Mhuire," sometimes with variations in the spelling, already has a presence in existing Mudcat Forum threads. So there is a question of duplication.

If members and moderators feel that strongly about it, then...well, I will leave it to them what action to take. My only motivation is to start a consideration of this song with the version that is published in the 1906 collection edited by Douglas Hyde. Other versions, and the collectors or singers who document them, are welcome with open arms here.