Inishmaan Aerodrome (IIA) has no lounge, and if you are asking about lounge access on the Aran Islands the honest starting point is that this is a small STOL airfield built for a short island hop, not a terminal with any premium space at all. Aer Arann Islands operates the route here, flying small Britten-Norman Islanders between the three Aran Islands and the Irish mainland on a schedule built around island life rather than connecting banks of jets.
The ground-side reality at Inishmaan is what actually shapes the experience: a tiny terminal building, a short walk across open apron to a nine-seat aircraft, and a flight time measured in minutes rather than hours. Travelers here are typically locals, day-trippers, or islanders returning home, and the wait before boarding is more about watching the weather over Galway Bay than browsing any amenities list.
Connemara Regional Airport, near Galway on the Irish mainland, is where Aer Arann Islands' island network actually begins, and it carries its own small-scale facilities rather than anything resembling a premium lounge. For a genuine lounge experience on this side of Ireland, Shannon Airport is the realistic answer, with its own Priority Pass and airline lounge options for travelers connecting onward internationally from the west of Ireland.
If Inishmaan is part of your Aran Islands trip, plan around its actual scale: a short wait in a small building, weather-dependent scheduling common to island STOL flying, and no lounge to fall back on either way. Save any real premium-lounge plans for Shannon on the rest of your itinerary, and check Aer Arann Islands directly for current schedules, since island flying adjusts around weather more than a mainland timetable would, and a delayed crossing over Galway Bay in poor Atlantic weather can reshape your whole onward connection plan for the day.