There is no direct train service from Sevilla to Lisbon.
You would have to take the AVE to Madrid and then the once daily overnight Lusitania Express from Madrid to Lisbon.
You best bet would be by coach.
There are two options:
1) http://www.alsa.es
This company currently operates 2 daily services between Sevilla and Lisbon as follows:
SEVILLA LISBON 15:00 21:15
SEVILLA(Prado) LISBON 23:30 06:00next day
2) EVA Transportes/DAMAS Change and buy ticket in Faro
Sevilha Faro 07:30 10:10
Faro Lisboa 11:00 14:15
Sevilha Faro 16:15 18:55
Faro Lisboa 19:00 22:15
