Firstly, forget car hire.
The cost of inter-country drop-offs in Europe is exorbitant.
Secondly, there is no direct train between the two cities - you would have to travel via Madrid which will take hours.
As regards flights there are no low-cost operators on the route. Vueling was supposed to start last December but have dropped the route due to business problems. Only TAP-Air Portugal flies the route and one way tickets are currently priced at circa € 300 per adult.
The most reasonable way to travel between the two cities a present is by long distance coach.
There is a daily departure from Lisbon Sete Rios Bus Station (Metro Jardim Zoologico) at 11:00 arriving in Seville Plaza das Armas at 19:00 (Spanish Time) Daily.
Prices at present at 40 Euros one way. The trip takes about six hours and routes through the Alentejo, Algarve and Costa da Luz to Seville.
The operator is ALSA. Website here - www.alsa.es.
You may be able to get a combination of low cost fares Lisbon - Madrid - Madrid - Seville. However, no one operator apart from Iberia operate both sectors and the latters current one way price is € 354.00
In summary, I recommend that you consider the bus which should be a more relaxing trip for all and you get to see the countryside.
