I run a factory. Who is responsible for the LPG pipework between the LPG tank and the factory?

You are. As with internal pipework, the LPG pipework between the LPG tank and the factory is the property of the consumer. Pipework does not have an unlimited life and steel pipework in particular will eventually deteriorate and leak. Such a leak may result in a fire or explosion if the LPG accumulates and an ignition source is present. In order to ensure the continued safe operation it needs to be inspected and, in due course, replaced.