I agree with Fred McCormick in not ever having heard of any music for "Caoineadh Art Uí Laoighre", except for Peadar Ó Ríada's composition which was first performed in 1998 and subsequently released on CD in December 2005.
Fred's suggestion that the tune might have been the superb "Lament for Staker Wallace"(a great favourite of mine) caused me to recollect that Art Ó Laoighre had returned to Ireland with the rank of captain from the army of Marie Theresa of Austria and that perhaps the tune that our mad Piccolo player might be thinking of is another favourite of mine "The Wounded Hussar"? I know that a wonderful rendition of this slow air was recorded on audio cassette, in the 1970's by accordionist, Tony Mac Mahon.
I hope this helps.