The Metro in Lisbon only starts operating around 06:00 in the morning.
For those staying downtown in the areas of Cais de Sodre, Rossio & Restauradores and wishing to get to the Airport to catch a flight, there is the Carris night bus route 208 that leaves from Cais de Sodre and passes through Praça Figueira, a short walk from Restauradores.
As it goes all round the houses, one should probably be better to getting an early departure.
Timetable here: http://carris.transporteslisboa.pt/pt/autocarro/208/ascendente/
Bear in mind that this takes one to Terminal 1.
If leaving from Terminal 2, one then needs to get the bus shuttle from T1 to T2.