Is it better, less expensive, faster, etc. to fly to Lisbon from Sevilla or take the train?
Surely faster. You'd have to take the train to Madrid, and then the night train to Lisbon. See bahn.de for schedules.
Use whichbudget.com to search for the lo-cost inter EU airlines. Pay attention to the airport/ airports that these airlines use. (some require extensive transportation arrangements) In general, all of the lo-cost airlines have VERY restrictive baggage rules; size, weight, etc. When they say ONE carry-on, they mean one item...ONLY! But, you can save hundreds of $$, and sometimes fly for many $$$$ less than taking the train.
We had originally planned to rent a car and drive so that we could see more of Portugal, but the cost of renting a car in Spain and dropping it off in Portugal is exorbitant. So, now on to Plan B...how to get there? If we can get from Sevilla to Portugal, we can rent a car, but it seems that getting from Sevilla to anywhere in Portugal is hard to do.
Where in Portugal do you want to go? There is a bus to the Algarve - see http://www.eva-bus.com/novo/ - and others to the border at Ayamonte.
We could possibly rent a car in Faro. I had thought a bus was possible, but did not know how to find info on bus schedules. Thanks so much for that information.