The minister responsible for Parks Canada is the minister responsible for the act, which means he is responsible for the administration of the act. It does not imply and the act doesn't say that all lighthouses that are designated should be transferred to Parks Canada. So coast guard would remain the custodian of lighthouses that were designated that it owned.
It means Parks Canada is responsible for running the program, for making sure the petitions are received and evaluated and the minister makes decisions about designation, and in assisting the department in any conservation, assisting in terms of professional expertise to the department in terms of conservation work that is done on designated buildings and on conditions related to sale or disposal.