Just wanted to follow-up on this, In the end, there was no option to use the Arrival's Lounge (as folks here suggested). I asked once about it, and they just suggested the Dali Lounge, so I gave up and we went there.
In fact, with your itinerary, technically you cold not even have used the arrivals lounge if you were an IB+ elite (because MAD was not your final destination).