There were, of course, other Inchiquins, such as Murrough O'Brien, 4th BARON of Inchiquin, who strangely enough is associated with Clare, noted above.

Considering his sad demise, in battle, at Erne, I would tend to like 'Lord Inchiquin' to be a lament of him . . . [?]

As a small note, Lord is a title for Barons, not earls, although the 4th EARL of Inchiquin was also 9th BARON of Inchiquin; he was also Grand Master of the Premier Grand Lodge of England, 1727, though I don't know why such a great song would be written about him.

See below for further info on the Inchiquins:

Regards
Lee
Liverpool, New York

http://mostyn.com/Genealogy/Father/Family/WC06/WC06_049.HTM
Children
Dermod O'BRIEN 5th Baron Inchiquin
Teige O'BRIEN
Slaney O'BRIEN
Honora O'BRIEN
Mary O'BRIEN
Margaret O'BRIEN
More O'BRIEN

http://www.clarelibrary.ie/eolas/coclare/history/frost/chap14_expedition_of_earls.htm
For some years peace prevailed in the county [of Clare], a most unusual circumstance. The Burkes of Galway, broke out into rebellion, and the Earl of Thomond was summoned by Sir Richard Bingham to aid him in bringing them into submission [1590]. Again, in 1593, in 1596, and in 1597, the Earl's services were called into requisition to help the English. He left Ireland for England, in January, 1598, and remained there the whole of that year. Before his departure, he had been solicited by the Lord Justice to co-operate against O'Donnell who had revolted in Ulster. Murrogh, fourth Baron of Inchiquin, also was required to give his assistance. They promptly responded to the call, and marched their forces, under command of the Governor of Connaught, towards the North. In attempting to cross the river Erne, they were met by the army of O'Donnell, and the Baron of Inchiquin received a bullet in the arm pit, through an opening in his coat of mail. His body was carried to Assaroe, and buried in the abbey of that place. The Franciscan friars of the monastery of Donegal laid claim to the privilege of having his remains repose in their cemetery, and appealed to the bishops of Derry and Raphoe. Their demand was acceded to, and the Baron's body was re-interred in Donegal.