I am really confused! Please help! Me and my son just arrived to Rome. We took a flight from Newark through Lisbon. When arrived to Rome airport, we followed the crowd and ended up outside. No security, passport check or stamps... Our passports were stamped in Lisbon. What should I do? Is it going to be a problem?
You entered the Schengen zone in Portugal then moved within it.
You're fine. It's over.
Going from the US to Italy, you go through passport control (control of people) on your first entry into the Schengen Zone. In your case, that was Lisbon. So your flight from Lisbon to Rome was treated like a "domestic" flight - no passport check. Once in the Schengen Zone, there are no routine passport checks between countries (although they still can occur - just not routinely).
You go through customs (control of goods) at your destination country, so you did go through customs in Italy. But you probably didn't see it, because going through customs in Europe merely entails going through the "Green Channel - Nothing to Declare" lane. Unless you choose to declare something, or are stopped for an inspection, you just keep going and exit the airport.
You go through immigration and passport control at your first point of entry. For you it was Lisbon. Then you are in the Schengen zone and free to move around without going through a check point. As the other poster stated you simply go through customs at your last point but you probably just walked through the nothing to declare area and out to the exit for the airport without even knowing it.