Long distance bus travel on the Iberian Peninsula is very reasonably priced, comfortable and safe.
avanzabus.com operate three daily services between Lisbon Airport, Lisbon Gare Oriente bus station and Madrid Estacion Sur bus station. Transit time is just over 8 hours allowing for the one hour change to Spanish (CET) time.
alsa.es also operate between Lisbon Sete Rios Bus Station and Madrid but it is an overnight service,
anibal.es also operate from Lisbon Gare Oriente to Madrid but their website does not currently provide clear details of frequencies.