That's not entirely true. If you arrive in First and depart in Club, you can use the first lounge. So I can see where the OP might think it would be possible to use the Biz lounge if arriving on a short haul biz flight.

But in any case, post #5, scenario 3 of this thread indicates that the OP won't have access. My suggestion is to enjoy the biz lounge in Madrid and eat something there.