Portuguese officials love rescheduling appointments at the last minute, so you'll end up making twice as many trips as you planned. The commute from Lisbon to Oeiras during rush hour turns into pure hell with all those roundabouts and narrow streets. Getting stuck in traffic when you're already late for a meeting with some licensing officer puts you in a foul mood for the rest of the day. Better to base yourself locally and avoid that mess altogether. You can rent a car in Oeiras right here
https://getrentacar.com/en-US/portugal/oeiras . Pick it up near where you're staying and you won't be wasting half your morning just getting to the first appointment. Returns are straightforward too since you're already in the area when wrapping things up.