If you have a look in the Iberia section on FT you will find plenty of discussion about the Iberia lounges in Madrid T4.
I don't think you would have access to the arrivals lounge. I could be wrong on that, but I believe/understand it is Iberias own tier members only (plus those flying in the business cabin). Its not a oneworld (rules) lounge.
I'm assuming it is a direct Iberia Express operated flight MAD-DUB?
Anyway, your longhaul flight will arrive into T4S (the satellite terminal), but your flight to Ireland will normally depart from the main T4.
Given that you are not departing from T4S you will head down to the shuttle train to take you to T4 main, where you will immigrationally enter the Schengen area of which Spain is part.
You will be in T4(main) - where the main gate area is Schengen cleared.
You will have access to the Iberia Dalí lounge in T4 main - which is up a level giving you a close up view of the rather stylish roof of the airport.
(If you have a prioritypass card, etc, another option would be the 'La Revoltosa' lounge run by AENA the airport operator.)
Note: T4S arrivals and departures are segregated, so you will not have physical access to the Ibeira lounge in T4S when you first arrive, and they will only normally admit people traveling on flights from the gates in that part of T4S.
Note2: As Ireland is not actually part of the Schengen area, when you head to the gate you will head to one end of the main T4 terminal, where a small number of gates are separated from the others. To get to these gates you will then go through a quick immigration exit from Schengen area.