If you plan to fly with your pet with Lufthansa Airlines, make sure you know about Lufthansa Pet Policy before you book a flight ticket. There are only a few things that you need to know about their pet policy. They allow small dogs and cats in the cabin, as long as they are in a carrier that can fit under the seat in front of you. you can book Lufthansa flights on the phone by calling their pet policy number. An agent will assist you to book your Lufthansa Flight.