ALSA does Lisbon-Seville directly for 35€, 7h15 duration one way.
You can also give
EVA (Algarve Bus company) a try.
The website is a tad weird as it doesn't generate the pdf's in english once you search for a route, but the info is there.
Anyway the route would be:
Lisbon-Faro up to 6 daily frequencies in the summer for 19€, duration 3h15, approx 270km.
Faro-Sevilla 2 daily in the winter (i guess summer would have more;16€; 3h40; approx 175 km.
You can also take a train from Lisbon to Vila Real de Santo António, cross by ferry to Ayamonte, Spain, which is fun and breaks the routine (~15 minutes), and then take a bus to Seville. I'll try to give you a few links for this.
EDIT: just found this very good
link with plenty of detail of travel between Portugal and Spain by rail/bus. Quite a few similar suggestions
If your travel permits I'd spend a few days on Algarve's coast before going to the scoarching heat of inland Seville. There are quite a few semi hidden gems around this east Algarve Coast.
Cacela-a-velha being one of them. The seafood, fish and wine in this stretch of coast are just amazing.
GBM