If perchance one doesn't want to use the Metro between Lisbon Airport and Gare Oriente Station in Lisbon, local Carris Bus Route 744 operates this route throughout the day.
First bus is a 05:35 and Last one just after 20:30.
I've used it a couple of times when coming up from Lagos and the Algarve on the RENEX.pt overnight "Redeye" arriving at Oriente at 05:00.
Overnight Carris Night Route 208 also operates the route between Gare Oriente and the Airport.
Bear in mind these buses may not have much space for big bags as they are local buses.