We have a layover in Lisbon arriving at 10 pm and not flying out until 10:45 am the next day. What would you recommend?
Your heading says 9 pm and your text 10pm!
If you arrive at 10pm, it will be 10.30 /10.45 before you are out of the airport. The following day, you will have to be back at the airport at say 8.45 or 7.45 if you are flying to the States. It takes 40 minutes plus to get into Lisbon. As most places would be closed, I would just take an airport hotel room for the night.
Find a nearby hotel with shuttle service
This from --http://www.lisbon-airport.com/hotels.html
There are no hotels located within Lisbon Airport but due to the relatively short distance to the city center, several hotels are located nearby.
Some of the hotels located nearby the airport include the Holiday Inn Lisbon Continental, Radisson SAS Hotel Lisboa, Marriott Lisbon, the NH Campo Grande, the Hotel Tivoli Tejo, the Barcelona Hotel, and the Hotel Olissippo Oriente. These are all within 15 minutes from the airport and can be accessed with relative ease. The various rates for these hotels may be obtained from their websites.
Most of the hotels within the vicinity of the airport offer free shuttle bus services to and from the airport. One may also choose to go to the hotels via taxi service which can be obtained from the airport. You may also make prior arrangements with the hotel to have a taxi pick you up from the airport and take you to your destined hotel.