Learned this recently from the playing of Derek McGinley on The Fiddle Music of Donegal: Volume 3 (http://www.mustrad.org.uk/reviews/fmd3.htm). There is not much about it on the internet, it comes from the playing of Jimmy Lyons in Donegal, there is a clip in the Comhaltas archive: http://comhaltasarchive.ie/search?q=composition_id%3A4501
Inishmurray is County Sligo’s holy island with an ancient monastery within a cashel, containing Ireland’s oldest stone church and many engraved cross slabs and pillars including the famous Cursing Stones. The modern village was evacuated in 1948. The Inishmurray hornpipe seems unknown around Sligo; Jimmy Lyons worked for a time as a fisherman in SW Donegal.
Take a virtual tour of the Cashel here: http://www.voicesfromthedawn.com/inishmurray/