Hello Chiara and welcome to the community!
I was surprised to see that Lufthansa would not allow you to take your instrument with you 
especially when it is obvious you would be the owner. Was is due to its size or materials?
As far as I know, there was a restriction with rosewood but it has been lifted from finished musical instruments.
If not purchasing directly in Japan or in your own country, I would be extra careful about materials such as real tortoise shell and also ivory (most often found in bachi, itomaki, koma). These might not get selled to you or shipped or if so, they might get seized.
My two cents. 
Good luck and I hope that you´ll get the shamisen you like real soon!