Yes, Madrid-Barajas Adolfo Suarez Airport (MAD) has lounges, and plenty of them: this is Iberia's home hub, concentrated in Terminal 4, with a wider spread of independent and airline lounges across the airport's other terminals as well. If you searched madrid airport lounge or barajas lounge, the honest answer is variety rather than a single answer.
Iberia's own VIP lounges anchor the Terminal 4 experience, serving Iberia Plus elite members, qualifying premium-cabin passengers, and fellow oneworld alliance elites and business or first-class travelers, since Iberia is a core oneworld member and T4 functions as the alliance's Madrid gateway. These are the most reliable lounges at MAD if your ticket or status lines up with Iberia or a oneworld partner.
Beyond the Iberia network, Madrid also has independent pay-in lounges spread across its terminals, open to travelers willing to buy a day pass regardless of airline, and some of these accept Priority Pass and similar memberships, though acceptance varies by specific lounge and can change, so confirm your exact entry point before you fly rather than assuming blanket coverage. Certain premium credit cards also carry lounge-program benefits that may apply at select Madrid lounges; again, check your card's directory for Barajas by name.
Because Madrid is a genuine major hub split across multiple terminals, access modes are the real story here rather than a simple yes-or-no. Iberia and oneworld status covers Terminal 4 most reliably, independent pay-in lounges fill the gap for travelers without airline status, and card-network or Priority Pass coverage sits somewhere in between depending on the specific lounge and current terms. Match your credential to your terminal before arrival, and treat any online listing as a starting point to verify rather than a final answer, since a hub this size updates lounge details more often than a small regional field ever would.