Measure the diameter of the hole and the thickness of the door.
Find a piece of scrap wood the same thickness as the door and a hole saw blade the same size diameter as the hole. Fit an electric drill with the hole saw blade.
Cut a hole in the piece of scrap wood. Sand the edges of the cut circle down one-sixteenth of an inch with a piece of medium grit sandpaper until the wood just fits into the hole.
Apply a bead of wood glue around the edges of the circle and press it into the hole in the door. Allow the glue to fully dry according to package directions.
Press the end of a tube of wood filler against the space between the patch and the rest of the door. Squirt a small amount of filler over the space and smooth it out with a plastic putty knife. Allow to dry.
Sand any bumps smooth with fine grit sandpaper and paint over the area.
Measure the diameter of the hole and purchase a lock filler plate in the same size.
Insert one side of the lock filler plate into the hole on one side of the door and the other side of the plate into the hole on the opposite side of the door. Press until the mechanism clicks together snugly.
Insert and tighten the trim plate screws to secure the filler plate.