I used to do a lot of airline travel and brought my big box with me then.....

After 2001 all the rules regarding luggage carried by the airlines changed. Though each airline has relaxed their policies over the years, the final decision is made by the customer service supervisor /manager AT THE TIME OF DEPARTURE. This is the case with most airlines in North America, Europe and Asia flying into North American airspace. ANY item that is deemed a safety risk to the aircraft, crew or passengers will not be allowed. There is a chance that your big box may be accepted but DO NOT EXPECT IT. Lufthansa is no different than any other airline when it comes to baggage policies. If you want to ensure your toy arrives at your destination ship it via freight well ahead of your planned arrival.

Don't shoot the messenger...this is simply what has been told to me by various airlines ( Westjet, Alaska, AirCanada, British Airways, American Airlines, United Airlines )

Cheers
Dean W.