Transportation from Lisbon to Seville

Because of Spain's history their rail system is not as well developed or integrated with surrounding countries. I would consider the bus system. Spain has an excellent bus system. We probably use the buses more than trains when we are in Spain. Drop fees in other country are expensive because someone has to drive the car back. One possibility might be is drop the car in a border city, cross the border and rent within Spain. Drop fees within a country are generally very reasonable or none. And it just be less hassle to use one of the discount airlines.

If you only have one day to get from Lisbon to Seville, driving would have you stick to the motorway most of the time anyway (too slow otherwise). So, you should fly, without regrets.

Ground transportation links between Portugal and Spain are limited and infrequent, as you have discovered. At one time there was an overnight train between Lisbon and Madrid; I don't know how comfortable it was, but it existed. That is not running now. I think in your situation flying is by far the best solution. If you had more time, you could take the train south to Faro and switch to a bus (infrequent), or you could take multiple buses. I believe the crossing in the north (from Porto up to Santiago de Compostela/Galicia works a bit better, but I believe it is still awkward. One can only assume that not many Spaniards vacation in Portugal, or Portuguese in Spain.

Transportation between Spain and Portugal is not the best. There are good reasons for that.

I would fly from Lisbon to Seville. Look at TAP Airlines. We have flown them many times. They are always reasonably priced, on time, clean airplane, and good service.