There is no train service directly between Seville and Lisbon.
As from 1st December 2007, Vueling will operate Seville - Lisbon on Monday's, Wednesday's and Saturdays.
TAP Air Portugal have announced that they will also operate the route from Autumn but have not confirmed dates yet.
At present the only direct way by public transport is by bus.
There are two companies currently operating the route.
Alsa and apparently Casal. (The latter does not have a website and I haven't been recently to Seville nor Gare Oriente to be able to confirm.)
You can find the Alsa timetables here on cubsur's excellent site:
Go to the bottom of the page.
http://thomasallen.home.sapo.pt/travel/001.htm
Also see the following blog articles page:
http://barlaventostravelblog.blogspot.com/search?q=seville+lisbon
