Hi, Debra,
Last year I took the bus from Lisbon to Sevilla. It was a long, boring all day affair. Leaving around 9 am, arriving around 7 pm (that includes an hour time change, but still, it was a long trip with an hour's stop in a godawful highway rest stop). There are several bus companies that provide service from the Oriente station (which is the station one closest to the airport), Eurolines is one of them,
http://www.eurolines.es/ep35/w2selciudad.csp. Alsa and the Portuguese national bus system Rede Expressos also provide service jointly. I don't remember the price, but I am pretty sure it was around 50 or 60 E.
You might also consider flying. Both Spanair and TAP fly nonstop Lisbon to Sevilla, and if you get your ticket far enough ahead, you might get it for as low as 80-90E.
Trains are not really an option, you have to go through Madrid.
Good luck with this, when are you walking? Laurie