8 he Layover in Lisbon

At approximately six miles, the Lisbon Portela Airport is close to Lisbon's city center. That may encourage you to research areas of interest in Lisbon and, perhaps, arrange for a private walking tour carefully designed to meet your interests. A taxi ride to a designated meeting point with your guide might be wise. The RS "Portugal" guidebook lists several recommended guides in Lisbon.
The recent RS "Lisbon" video has Rick taking what appears to be a "food tour" with guide Cristina Duarte. That looks like a fun way to get some exercise, see some of Lisbon's sites and sample local cuisine.

I would take a bus or metro to Rossio Square, the flat center of town, and start there. (Metro requires a change somewhere, but it's pretty simple.) Use Google maps on your phone if you have one to navigate public transportation and walking directions, in real time.
You could take a taxi or Uber (they operate in Lisbon) to save time, I guess.

You might also find out when a couple of the free walking tours start; maybe your timing will be right and you can just join one, at least for the first part. If you don't take a walking tour, find a self-guided one online and walk up to a couple of the viewpoints. Lisbon is very hilly. Alfama is the most interesting neighborhood and the oldest. Have a couple of pastel de nata's (pastries), the delicious signature treat of Lisbon (or Belem actually). If it's rainy, visit the Gulbenkian art museum.

I rarely leave airports even with longish layovers but your case sounds doable. A taxi to/from will save a few minutes, which in this case is precious so I'd do that. Look in guidebooks for the suggested walking tours and walk from Rossio down to the waterfront, up into the Alfama, over to the castle and back down. That plus lunch will probably be all you have time for. Cafe Nacional is right off Rossio and has amazing food at amazing prices. Photos #30-32 in this gallery.

This is all wonderful information! Thank you all!

We like historical things and just roaming on our own, but I've never done a walking tour to know if we'd like it or not. I'll check into those. Going around to a few places and having lunch and then back to the airport sounds PERFECT though!

And thank you for the food suggestions! We love good (cheap) food!!!

Hopefully the weather is nice, but if not I'll check out the museum! thank you for the suggestion!

"I would plan to get to the airport about 2 hours prior to our flight,"
Smart.

You need to understand the airport departure process.

1. Getting thru security. Usually quick. 10 minutes.
2. Walking towards your gate thru all the shopping. 10 minutes. Seeing the lying signs that indicate your gate is just a few minutes away.
3. Emigration. The queue is usually in the 45-minute range.
4. Walking towards your gate. 5 minutes.
5. At the gate security checkpoint (yes, another one). 5-10 minutes.

Total time from curbside to jetway is 1.5 hours.

I had that issue flying back to the US last time. We had a layover in Dublin, which our flight was already late for by almost an hour. Then I found out that I was randomly selected for a thorough screening... Took forever! And had to unpack everything in my backpack that and get swabbed (including my hands and feet) then just sat there waiting. Then we ran around the corner to find a HUGE immigration line...thankfully US citizens had a seperate like than EU and we got through very quickly. I was the last person in line for the plane boarding...terrible!

I've had too many close calls to take chances. 2 hours would be the minimum time I would plan to give ourselves after that. Talk about stress!

I would spring for a taxi to and from the airport. Use Rick's audio guided Lisbon City Walk for a sampling of the neighborhoods and sights.
Have lunch and be sure to try pastel de nata.

Definitely take a taxi or Uber into the city to save time. However, the waiting times for taxis at arrivals is sometimes quite long. To save time, take the escalator in the arrivals hall up to the departures area. Turn left from the escalator and go out the doors in front of you. You will see taxis dropping off people for their flights and can grab one right away. It could save you up to 30 minutes.

I would suggest taking it to Praca dó Commercio, right on the river, to start your wander. The Time Out Market is a great place for an early lunch with a number of Lisbon’s top chefs having places there. But don’t go after 12:30 due to crowds.

Read a bit on what area appeals to you most, but try to get to at least one miradouro for the wonderful views that are Lisbon.

Check with your airline, but most flights to the USA require you to be at the airport 3 hours before departure. Allowing for getting out of the airport, if you are on time, you probably have about 4 /4.5 hours to play with, not 8 hours. That’s enough time for a quick trip into Lisbon.