The most direct route by public transport from the Lisbon Four Seasons Hotel to Parque das Nações (Gare Oriente) would be to walk to Pombal Metro Station and then take the Linha Amarela (Yellow Line) in the direction of Odivelas.
At the second stop, Saldanha, change to the Linha Vermelha (Red Line) in the direction of Aeroporto and disembark at Gare Oriente Station. Follow the signs for the Centro Comercial Vasco da Gama, walk through this shopping mall and then you are then in the area of Parque das Nações
The metro runs till after mid-night.
Lisbon Metro: http://www.metrolisboa.pt/