Lufthansa provides extensive Information about traveling with Pets on their Airline on their own Website here.
This is just a Summary of Conditions and Charges. Please confirm Current Prices with Lufthansa.
Pets in the cabin
Lufthansa accepts small dogs and cats transported in the passenger cabin if the weight of the pet (including container) does not exceed 8 kg. The pet must be stored in a waterproof and bite resistant container of maximum 55 x 40 x 23 cm. The container must be stored under the seat directly in front of the passenger.
Prices
Pets are not included in the free baggage allowance of the passenger and a fee must be paid:

• flights within Europe and to third countries – € 50.00
• intercontinental flights – € 70.00

Prices for the carriage of animals as excess baggage in the cargo hold
The price for the carriage of animals as excess baggage in the cargo hold depends upon the route as well as the size of the transport container. The price is per flight direction, i.e. also on Lufthansa connecting flights, and is charged only once (e.g. on a flight from Hamburg via Frankfurt to Madrid). It must be paid again for return flights and stopovers (2).

Payment for transporting your pet should be made at the check-in counter or at the Lufthansa service counter at the airport. In addition to your pet and its transport container, you can, of course, also use the free baggage allowance included in your ticket.
Prices for transporting animals as excess baggage in the cargo hold
Pets are not included in free baggage allowance, but are considered excess baggage. The amount of the fee depends on the size of the cage:

• Transport Container 1:
  • Flights within Europe and Third Countries – € 100.00.
  • International Flights – € 150.00.
• Transport Container 2-4:
  • Flights within Europe and Third Countries – € 200.00.
  • International Flights – € 300.00 .

The information contained is believed to be true, but we have made no attempt to verify it.Please check with the relevant Organization.