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Per the oneworld lounge access rules, you'll have access given that your international segment was in Business Class:

http://www.oneworld.com/ow/ffp/loung...-access-policy

I'm not really familiar with the lounges in MAD (I didn't need to take a shower the one time I was there), so hopefully someone else will let you know about the available amenities.

Peace.

Since you're connecting to domestic IB, you'll exit your flight and make your way through Passport Control in Terminal 4 Satellite, then descend in the elevators to the underground train to Terminal 4. Back up the elevators then you will re-enter Security and can head to the Sala VIP Dal� lounge, hosted by Iberia. They have plentiful showers there, you just request a key from the front desk and they keep your boarding pass as collateral. The showers are fine, my only complaints are that the rooms are quite small if you have more than one carry-on with you, and even when I take a cold shower, I still emerge from the shower room sweating because the lights are very hot and there are no ventilation fans. If you like to take a hot shower, it will be pretty much like a hot sauna in there when you are finished.

Sounds like the showers in the BA lounges at LHR T5. I could never understand why they installed pre-fab showers in such a nice complex.