The protein bank is a facility, or likely an entire organisation of such facilities, present upon the Cluster that harvest organs "for purposes that serve His Shadow", such as making robotic drones and feeding the Lexx.
Having to donate to the protein banks is a primary form of punishment for any infraction against the, often extreme, laws of the Cluster. Typical punishments will involve the removal of redundant organs such as an eye, a kidney, a lung, or a testicle, however criminals convicted by the holographic courts will often be punished by having their "individual life terminated" and all useful organic material sent to the protein bank(s) by a specially designed cutting device that removes all major organs simultaneously.
Ultimately however the true purpose of the protein banks are in fact to provide a source of food for the Lexx, and likely also the Gigashadow. To this end the punishment for even minor crimes is often excessive, resulting in most true criminals being sentenced to death via protein reclamation, and even minor infractions may result in being sent to the protein bank as a disciplinary measure. The end result is a significant amount of harvested parts, shown being routed onto conveyor belts for the feeding of the insect(s).
The protein bank appears in Lexx 1.1 I Worship His Shadow, in which Stanley Tweedle is sentenced to punishment there, however he chooses to masquerade as a security officer charged with bringing in another person, and upon learning the intended punishment attempts to avoid his fate. He later returns to the protein bank, deciding that losing some redundant parts is preferable to death, but is too late and finds the branch to be closed resulting in a kill order.
During the same episode, criminals restrained upon large metal slabs are shown being delivered on rails from a penal transport to the holographic judges. Most are sent along the rail to protein reclamation, where the slab slots into a wall recess featuring a chute and several cutting implements on organ-shaped circuits, separating major organs from the victims in a matter of moments. The organs are shown to be collected in bags and fed onto large conveyors leading to the mouth of the Lexx. It is unknown if the rest of the body is harvested or simply discarded.