From the Lufthansa website:
Your arrival
The special First Class Service starts right away when you arrive at the First Class Terminal Frankfurt. The parking of your car or the return of your rental car will be done for you by Sixt Valet Service. And naturally we will also make sure that your baggage is forwarded.

http://www.lufthansa.com/it/en/First-Class-Terminal-Frankfurt?blt_p=IT&blt_l=en&blt_t=Info_and_Service s>At_the_Airport&blt_e=Content&blt_n=Related%20top ics&blt_z=First%20Class%20Terminal&blt_c=IT%7Cen%7 CInfo_and_Services%3EAt_the_Airport%7CContent%7CRe lated%20topics%7CFirst%20Class%20Terminal