Auto Rental

One way that I would research that would be to search on Google Maps for "car rental near Lisbon" and zoom in to find a balance between what is closest to your hotel and to a main road out of town. Of course, going out to the airport is always an option. The larger agencies have many offices and you need not return the car to the same place. Then, if you go to search for prices through the agency directly or through a consolidator like Auto Europe, you have a better idea of the locations that they might just list by address.

You might want to consider taking the train to Evora and picking up the car there. The train from Lisbon to Evora is easy and inexpensive. I’ve picked up a car in Evora and, though you will need a taxi from the train station, it’s easy.
Dropping it off before you go back to Lisbon - I checked a couple of the towns closer to Lisbon but Cascais seems to be the only one with an Auto Europe pickup point. The good news is that the Europcar office is pretty much across the street from the train station, making it very convenient to get into Lisbon on the train. Europcar is the company Auto Europe uses in Portugal.

I’m planning this as well - leaving Lisbon for Evora then to Coimbra and Porto and returning to Lisbon. There are numerous places in Lisbon away from the airport so I am looking for something closest to where we are staying on the east side of the city for easier exit to Evora. We’re returning to stay at the same place in Lisbon for 2 more nights so this will be convenient. I was looking at Avis to use a discount option I have and there are about 4 places. So you might think about what car rental company you plan to use and just google car rental in Lisbon to see all the options. I might consider the train to Evora idea too so thanks to their others commentor for that suggestion.