For example, the LLC will provide no protection for the pilot (doesn't mater if the pilot is associated with the LLC or not). That's not what it's designed for.
Depending on state law and how it is applied (none of this is foolproof) it will provide some liability for the members of the LLC (the owners of the company). But that is going to depend on a number of things such as how much the owners of the LLC participate in the direct management and maintenance of the airplane, how well the owners of the LLC treat the LLC as a separate and independent entity, and the terms of the leaseback agreement itself.
If you are contemplating leasing back an airplane owned by your LLC to an FBO, there are a number of issues related to and in addition to liability to be aware of. A lawyer in your state who understands both organizational structure and aircraft leasebacks is your best bet.