I went a few years ago so I can't remember how long it took but I'm fairly certain that the airport is on the metro system which would likely run late into the night, maybe 1am I guess. Search Lisbon metro system on google and you'll probably find all the information there.
Feel qualified to comment on this one as Lisbon is actually where Mrs Pullie & I went for our honeymoon back in 2010 - yes, airport not too far, a city beautifully divided between the old and the new. We stayed in the old town (mere few metres from the famous arch) in a Pombalina building designed & built to withstand earthquakes ! Loads to see and do, and as others have said get to the places (e.g., Cascais) you can easily reach in 30 minutes via their excellent public transport. Try and get to Luz and visit Benfica FC as well, great stadium tour. We were there in early July that year and it was 43 degrees, which even given their lovely dry air climate was a little hard to take. Overall though, brilliant place to visit.