1) If you are hiring a car in Southern Spain, it is probably best to return to Spain to drop it off, as one way car rentals between Spain and Portugal can result in serious "drop-off" premiums.
2) Lisbon has an excellent public transport system including trains, metro, buses and ferries. I have know Lisbon for decades but no longer drive into the town when visiting owing to the price of parking, traffic calming measures and the fact that it is easier to use public transport.
The old downtown (Baixa, Alfama, Graça ,Estrela etc ) is made up of many, often narrow, streets built on steep hills and winding curves. Not easy for driving.
It is probably better to leave the car in a car park at your hotel, at the airport or at Gare Oriente and take the Metro into town.
3) Bear in mind that in June, certain parts of Andalucia (Southen Spain) (e.g. Seville), can be nearly as hot as "Alice" during the day!
4) TAP Air Portugal operate daily flights from Lisbon to Seville. However, it is not a low-cost operator!
5) There is no direct train link between Seville and Lisbon.
6) There is a daily (twice at weekends) long distance bus service between Seville and Lisbon operated by alsa.es. Buses leave from Sevilla Prado San Sebastian Bus Station and Sevilla Plaza das Armas bus station.
7) eva-bus.com / www.rede-expressos.pt / damas-sa.es offers connections twice daily (four in summer) via Faro. Buses leave from Sevilla Plaza das Armas bus station. Tickets must be purchase separately for Seville-Faro and Faro-Lisbon. There may be some layover time.
