I would therefore recommend one of the two following options:
1) Hire a car in Madrid, Drive it to Jerez, then to Salema, then Lisbon. Put it in the Long Term Car Park at Lisbon Airport while you are in Madeira, then drive back to Madrid. Bear in mind that this routing will incur substantial tolls on the Portuguese Motorways. (Incl. electronic ones on the Algarve spinal Via de Infante A22.) Also bear in mind when renting a car to specify automatic if you are not conversant with manual shift.
2) If you want to do the trip by public transport, then take the AVE from Madrid via Seville to Jerez. Return to Seville by bus or train. Overnight in Seville. Take daily morning DAMAS/EVA buses from Seville to Faro/Lagos, in the Algarve. Either hire a car in Faro/Lagos or take the regular EVA bus to Salema.
2 days later, take the bus back to Lagos and then train/bus to Lisbon or drive from Salema to Lisbon.
Bear in mind a one-way hire will incur a drop-off fee. For this type of rental, I suggest Auto-Jardim or Europcar as both have offices in Lagos and Faro. In Faro bear in mind to specify pick-up at the TOWN office. Otherwise you will have to trail out to the airport to pick up a car.
