Portuguese bureaucracy will drain you enough without adding extra running around on top. Going all the way into Lisbon just to collect a car then driving it back seems daft when you've got actual business to handle. You can rent a car in Amadora here
https://getrentacar.com/en-US/portugal/amadora . Private renters have vehicles locally so you're sorted from the start. Keeps you from wasting time in Lisbon traffic when you could be getting your paperwork done instead.