Agree. Lisbon's airport is fairly easy to navigate, not far from the city, so it should be reasonably easy to pull this off. Figuring out what to do about sleeping will be your biggest challenge. Hopefully you sleep well on planes? If you can manage that, it will give you a small advantage.
Land in Lisbon, go from airport to hotel, see if you can check-in early, if not, drop bags and charge out the door, ready to spend the day, keep walking in the sunshine. Do a blitz/walking tour, try hard to stay awake until dinner, grab food, hit the bed, crash and burn. Set two or three alarms for the early morning wakeup, check out, off to the airport, jump through the hoops, nap on the flight to Prague/Budapest, wake up when the wheels touch down, pinch yourselves and ask each other if you really spent a day in Portugal or if that was a dream. It'll be an exciting way to begin your trip.
Edited to add: I could not disagree more about taking a nap in the afternoon. Don't! Having hours to kill in Lisbon at night is not a good plan - you need to be outside in sunshine, seeing the city. Try hard to stay awake until after you eat "dinner" - once you hit the sack, you will be down for the count (even if you tell yourself it's just a nap - you may wake up just in time to head for the airport). But if you can manage to stay awake until dinner (being outside in sunshine and fresh air is the best way to do that), then you will sleep VERY deeply, and once you do wake up the next morning, your body will be on European time. If you yield to the temptation to "just take a short nap" 1) it will probably be a much longer nap than you expect, and 2) you won't recover from jetlag for a couple more days. If you can tough it out staying awake in Lisbon until "dinner" you will be over the hump and good to go once you reach your destination.