According to oneworld lounge access rules, yes, you have access in MAD.
(Assuming you're flying AA from DFW-MAD, then IB from MAD-LIS?)
http://www.oneworld.com/ffp/lounge-access/
oneworld lounge access for First Class or Business Class travellers
Indulge yourself before departure in a wider range of airport lounges when you fly First Class or Business Class with a oneworld member airline.
Customers flying First or Business Class have access to the equivalent class of lounge regardless of their frequent flyer status. (First Class passengers may be accompanied by one guest travelling on a flight operated and marketed by a oneworld airline).
Customers flying in Economy class on the domestic or intra-European segment to connect to or from a oneworld longhaul First or Business Class flight can also use the lounge applicable to the class in which they are travelling the longhaul segment.
(underlining is mine)