AA does MAD-DFW, it's just getting to MAD, if LIS-MAD has irops it's FUBAR as the check in staff don't work for IB and can't do ticketing/anything really. Calling IB as non status is not gonna be fun....

There is no good solution in this no status/nonJ/2 kids/thanksgiving/doesn't speak Spanish problem

Maybe book LIS-MAD-DFW via AA, then at least if IROPS OP can call/twitter AA and the AA counter will be open at LIS for their 11am LIS-PHL.