I'm not sure where you got the idea that the train times are slow. There are several departures per day taking between 2,45 and 3, 25 hrs. Not bad for a 270 km trip that includes climbing through the escarpment out of the Algarve. Remember for downtown Lisbon you want to get of at Entrecampos Station and not Gare Oriente. This knocks 10 minutes of the trip.
I strongly recommend using public transport to visit Lisbon for the first time.
Currently, the local council in Lisbon is putting in place traffic calming measures in the centre of the city that is making it increasingly awkward to drive there unless you know where you are going. I have known Lisbon for 40 years and with the latest changes to the traffic system downtown even I had 'fun' recently when I was up there.
The motorway up to Lisbon is a toll road. For the price of a hire car, toll and fuel you could could get 6 return train tickets. It will take you you about 2.45 hours to drive to the Ponte 25 Abril bridge over the Tagus at the entrance to Lisbon.
Thirdly, by taking the train you will get to see a bit more of Portugal.
Lisbon has an excellent public transport system.
If you do take a car, try and get a hotel in the area of Avda. Jose Malhoa, which is just off the 1st Circular (which runs from the Ponte 25 Abril bridge) and near to Praça de Espanha and Sete Rios Metro Stations.
