Seville to Lisbon

AFAIK the best way is to fly. You can get to Evora by train from Lisbon. The journey is 1.5 hours, so it's possible - though not recommended - as a day trip.

If you are planning on driving a rental car, check the drop-off charges first.

There are also direct buses, 7 hours, traveling via Faro, not via Evora. www.alsa.es

How keen are you to visit Evora, wonderful as it certainly is? Getting there from Seville is going to take most of the day, unless you go by car. It's possible by coach via Merida. But it takes so long, it only makes sense if you plan to do the journey to Lisbon over at least two days. Otherwise, you won't actually see any of Evora before starting the journey onto Lisboa.

If you're planning to drive then it's pretty simple. Though you may then have the cost of hiring a car in Spain but dropping it in Portugal.

Budget or not, getting to Lisbon can be a chore. Alas, the previous advice that flying is the easiest is an understatement. I've found that no place in Spain is "close" to Lisbon!

It may not suit your own travel style, but we saw Evora (and some other big sights) on a highly regimented daytrip tour-bus excursion from our several-night stay in Lisbon. Although we were due to rent a car for travel north (Guimares, Coimbra AFAIR. Maybe we returned the car in Porto), we wanted to avoid annoying navigation issues, and did not want to rent the car until we were leaving Lisbon.

We included the Bom Jesu pilgrimage site on that car trip, and just this year, it was added as a UNESCO WH Site.

Flying direct to Lisbon on TAP is the easiest and quickest option unless you want to hire a car, which will be a one way drop fee of hundreds of euros. I googled buses from Seville to Evora and there seems to be one a week, but it takes all day, which, unless you have a very long trip, seems to be a waste of a day.

Ah, the dreaded Spain and Portugal combo question. This comes up about once a week on this forum, so you're not alone.

We in the US think of Spain and Portugal as practically one country, and a "natural pair" on a single trip. However, the transit links between the two are surprisingly skimpy, and combining them on a single trip is surprisingly difficult. There are a very few trains (often in the middle of the night), there are some buses (fewer than you would think, slower than you would think, and often requiring changes), and there are flights (more than you would think, to make up for the dearth of other options). You can drive, but a car rented in one country and returned in the other will have a high surcharge (can be several hundred euros).

Hence, the advice to fly from Seville to Lisbon, then see Evora from Lisbon (domestic connections within each country, often by bus, are much better than the international ones between them).

To find flights, use Skyscanner, then book directly with the airline to learn all the fees, rules, and restrictions: https://www.skyscanner.com/

To learn about bus connections, you can use Rome2Rio to find the bus companies involved, then go directly to the bus company websites (you may need Google Translate) to confirm schedules, prices, etc: https://www.rome2rio.com/map/Seville/Lisbon