What is a good way to get from Sevilla to Lisbon(May 2015)?
And, where would be a nice and interesting overnight stop?
The only direct public transportation is by bus (7 hours, www.alsa.es, recommended in Rick's guidebook) or flying (www.skyscanner.com, often not cheap, but take a look). There is not train service all the way through, unless you go up to Madrid and connect to an overnight train, which is not a fast or cheap plan.
Often the best way to go is by budget airline. The longer you wait to buy tickets, the more expensive they get.
We flew this route in October, via TAP. I think if I had to do it over again, I might do the bus. Considering the time and expense to get to the airport in Sevilla, and waiting around for the flight, and the time and expense of getting to our airbnb rental in Lisbon, it wouldn't have taken all that much longer to take the bus. And I have a feeling the bus might have been a more interesting experience.
How about taking the bus from Sevilla to Lagos on ALSA and then from Lagos to Lisboa on REDE EXPRESSOS (www.rede-expressos.pt) Each leg of that trip looks like around 4 hours.
When you log onto the bus sites, look for their English versions. When searching schedules, you need to put in a fake date that is no farther out than 2 or 3 weeks. Later, when it is close enough to your actual trip, you can put in the real dates.
Just fool around with different destinations from the drop down box, and maybe you will find another stop you like better.
Rome2Rio is a good site to get general bus, train and plane routing options.
We got a cheap flight years ago, although the little kids behind us kicked our seats the whole time, and their parents weren't on board with them -- so you may get what you pay for ;-)
Seriously though, if you go by land, Evora is a worthwhile place to stop - ancient Roman ruins, great square & town. Have dinner at the Pousada!