There are no direct public transport links between the Lisbon Alcantara Cruise Terminal and Lisbon Airport. The distance from the quayside to the nearest station is at least 600m. You would then need to get a train from Alcantara Station to Cais de Sodre station and then get the Carris Aerobus no 91 that runs between that station and Lisbon Airport.
If you have luggage I do not recommend this option. You will be better to get a taxi from the quayside straight to Lisbon Airport.
If you are in a group arranging for a private minivan shuttle may be the answer.
The following company may be able to assist you.
http://www.low-cost-transfers.com/lisbon-airport
