It states on the Iberia website that this is available only to those using Iberia services.

From the Iberia web site page, relating directly to the new Arrivals Lounge:-
We invite you to step in whenever you travel in Business class and your final destination is Madrid on a more than four hour long flight operated by Iberia.
Our Iberia Plus Platinum, Iberia Plus Gold and Iberia Singular customers will also have access when travelling with final destination Madrid on flights operated and/or marketed by Iberia more than 4 hours long, regardless of the class they fly in.

I would be very happy to be proved wrong that this does not appear to be available to other Oneworld travellers (so that we can use it after our next inbound American Airlines flight in Business!).