The BA flights from MAD leave from T4S. The lounge is an IB Lounge (but thankfully not run by IB). This is used by all eligible BA PAX. As it is in the non-Schengen area it is not such a pig-sty as the main T4 lounge and is actually a haven of tranquility with great views over two runways.
If you are there over lunch and don't forget that the Madrilenos tend to take a late lunch, there is a pretty good buffet at both ends of the lounge. Outside those hours there are sandwiches, mini-cabanos and pre-wrapped cheese portions.