Flights from Newark (EWR) to BCN (Barcelona, Spain) on TAP Air Portugal have stops in Lisbon, most of them arriving at 05:25. TAP actually offers free stopovers wherein you can book up to 5 nights in either Porto or Lisbon before continuing onward. So much time was unnecessary for me as I've been to both cities, but I couldn't resist the opportunity to take advantage and schedule myself a long layover in Lisbon.
Here's an idea of how to spend a 10 hour layover in Lisbon, Portugal when you arrive before sunrise!
A much more detailed and person version is posted on my person travel blog, if you are interested in how many times I ate pastries.
LIS is one of the easiest airports I've encountered. When you walk out of arrivals, you're greeted by cafes (skip the Starbucks, please), a Vodafone booth (cue up before it opens at 07:00), ATMs, and the Metro station just footsteps away. Meeting people there is easy and so is getting directly into town for less than 2 Euro. If you prefer to stick around the airport before your connecting flight, turn right from arrivals and follow the signs upstairs for check-in and departure gates (portas). You'll find essential shops before you get to security, but a full-on, high-end mall after you've passed through.
The free wifi in the airport works well as long as you are in an area that gets it. The browser prompts you to enter your e-mail address, but I use a fake one - it doesn't matter. Enjoy more carbs and pastries in the food area and update your social media.
Turn left out of arrivals and head all the way down and to the left to find the baggage storage area. For a very reasonable fee (under 10 Euro for most bags), you can safely store anything you don't need. For connecting flights under 24 hours, your baggage will automatically continue on to your destination, so make sure your carry-on has the essentials for your day. This isn't a locker system though - you'll leave your things there until you are ready to hold them again.
Lisbon's subway system is one of my favorites (though the local I spoke to on the plane thinks it's ineffective and unavailable). From the arrivals lounge, you'll walk through the doors to your right, outside, and down the escalator to the Metro. Buy a rechargeable Metro card from the machine. Each ride costs 1.45 Euro when you use the reloadable card, and a ride is over when you leave the subway system. In other words, you can transfer as many times as you need (within an hour) all on the same fare as long as you don't scan out and head aboveground.
The airport is the last stop on the red line, you only have one direction to travel.
While the Metro starts running at 06:30, you'll find that most of Europe doesn't wake up until well after that. If you're arriving before sunrise, I'd suggest enjoying an espresso and pasteis de nata inside the airport and then taking the subway to the first major stop, Oriente, to catch sunrise over the Mediterranean Sea next to the Oceanario (Aquarium). The view is marked by the Vasco de Gama bridge in the distance and cable cars suspended above the horizon. You'll be mostly alone, aside from homeless folks who have slept in the nooks of the corporate buildings, locals walking to work and runners. Stay cautious, but enjoy the view.
The Oceanarium is big, informative, and beautiful. If you'd like to go, buy your ticket online while you are still inside the airport. It doesn't save you money, but the line gets long right away, so you can move along quickly. Another alternative is to use the machine at the entrance if you can buy your ticket with a credit card. It's open from 10:00-18:00. Adult tickets are 13 Euro and the visit takes 1-2 hours depending on how much you read. I breezed through in 45 minutes because I was ravenously hungry and didn't enjoy the options at the onsite cafe.
Also at this stop is the massive Vasco de Gama mall, a vortex of time and places to spend your money. Be warned, it took me 15 frustrating minutes to figure out how to get out of this mall. There's a full food court, department stores, and it's directly cross from the Metro station.
Cais de Sodre
After you've enjoyed the Oriente area, I suggest taking the Metro all the way South to the Cais de Sodre station. You'll continue on the red line and get off at Alameda to transfer to the green line. Cais do Sodre itself didn't have anything that impressed me, but you'll have a view of the Ponta de 25 de Abril, Lisbon's Golden Gate Bridge.
There's always the opportunity to ride the Metro North from here, but walking the length of the city is less than 4 miles. I'd suggest walking North along Rue de Alecrim toward Bairro Alto. Check out the viewpoint at Miradouro de Sao Pedro de Alcantara. During the daytime, this small park is empty and quiet, but at night it turns into a beer garden atmosphere and sits next to the famous party area of Bairro Alto. It's also right next to Tram 28, which runs up and down the steep, graffiti art covered alley of Elevador da Gloria.
Head East a bit and you'll find a big open plaza with fountains in Praca dom Pedro IV. Take some photos, have another espresso, and watch pigeons. Facing northeast toward the plaza, turn right and take the pedestrian road toward Elevador de Santa Justa, which is sadly next to an H&M. This brings you to the Chiado area, full of swanky shops and fancy foodspots. The indoor shopping plaza here has a public restroom, if that coffee has gotten through you.
Continue North and you'll get to the historic plaza of Martim Moniz. It's a perfect place to people watch and grab a bite to eat. The area is lined with small shops selling everything you can imagine and graffiti on every corner.
Rua de Palma
This 4 lane road is the main artery of the city, connecting South to North. There are Metro stops all along it, but it's a pretty quick and easy walk up to the Alameda station, where you'll jump on the Metro to the airport. Take your time and tire yourself out before you head back to the airport.
You'll know you've reach the Alameda station because it falls just next to the long park of Parque de Fonte Luminosa, which stretches east and west across the highway. On weekends, you'll find lots of people hanging out on the grass. I'd suggest you grab a few more pasteis de nata for your flight, and you'll have lots of options for bakeries, or pastelerias.
This loose itinerary lasted me from about 07:00 to 13:30, giving me plenty of time to chill out in LIS before my 06:30 connecting flight. You'll only need to spend money on food and subway tickets, but you'll get a great overview of the charm of Lisbon!