From Lisbon, one runs down the A2 motorway to the Algarve, until Juction 10, then turn left onto the IP8 national road towards Ferreira do Alentejo, then Beja and then the old Roman town of Serpa.
Have lunch at the Molho Bico, just inside the city walls.
After lunch, run Serpa to Rosas de la Frontera, then Jabugal and then join la Ruta de la Plata E-803 till Sevilla.
Total trip time (non-stop) is about 5 hrs with Serpa located almost equidistant between Lisbon and Sevilla
According to google maps, the all motorway route via Evora and Badajoz is the fastest by about 20 minutes but by the time one gets ofs the motorways into either Evora or Tavira any time advantage is lost.
The good thing about the Serpa route is that it allows one to see parts of the Alentejo and Andalucia oft not visited by tourists.