I am trying to find an alternative to driving from Seville to Lisbon.
Someone else was trying to do the same thing recently and, I believe, they decided that a bus wsa the only alternative. You might use the search box
This probably isn't the best option but if you were thinking about visiting Porto, Air Berlin flies from Seville to Porto. Then it's about a 3 hour train ride to Lisbon.
Another option is by bus as there is no train between the both cities. You have to take a bus first from Seville to Faro in the south of Portugal and then take another bus from there to Lisbon.
Also, check TAP Air.
We took the bus a couple of years ago but went from Seville to Salema via Faro. We spent 2 nights in Salema, and then took a bus from Faro to Lisbon.
Tap Air flies between Sevilla and Lisbon (we went from Lisbon to Sevilla). We flew it about a week ago. It's actually a Portuguese Airline that's booked as Tap Air. They bus you out to an out of the way place and you use the stairs to climb up. No worries - it was a good flight.