There is no airport hotel in Lisbon.

But near, in Parque das Nações area (the ancient grounds of Expo 1998 exhibition) you have:

Hotel Art's VIP Executive (****) http://www.viphotels.com/

Hotel Tryp Oriente (****) http://www.solmelia.es/

Hotel Tivoli Tejo (****) http://www.tivolihotels.com/

Those are the nearest to the airport and you can enjoy Parque das Nações where remains some equipments of the Expo (like a big and very interesting aquarium) - http://www.oceanario.pt/site/ol_home_00.asp?popup=1

In Parque das Nações you also have the subway to downtown or a nice shopping centre if you need to do some shopping.

http://tinyurl.com/eq2mo

Bye and a good trip to Azores, Helena in Lisbon, Portugal