There is a Longstay car park just outside , I had to park there a few weeks ago when I picked a friend up from there, it was quite cramped.. I think it’s P3 .They were surprised I hadn’t booked, so you obviously can. ( see link below) I ‘ think’ it was one of the few places that had no height limit.
There’s that big campsite on the outskirts too, Lisboa camping.It has a security barrier. There is a bus right outside but I used taxi into Lisbon.Be careful not to get caught in the Lisbon rush hour.