A customer had to repair the lock on his bathroom door, and cover the damaged bathroom door from forcing it open.
For your damaged bathroom door, there are brass plates that wrap around both sides of the lockset. One brand, Mag-Plate, comes in tall and short patterns that vary in height from three to eight inches. They come in different sizes for different door thicknesses and knob backsets. Knob backset is the distance from the edge of the door to the center of the knob. Older homes are 2-3/8 inches while new and replacement doors usually measure 2-3/4 inches.
These plates can be a little imposing when used on an inside door but it is easily overlooked when compared to the price of a new door. Usually they are utilized on main entrance doors where the relatively large brass surface adds a distinctive statement while adding strength where an old lockset existed.
To repair the lock is harder. As handy as Mag-Plates are, they cannot enlarge the hole in the door to 2-1/8 inches. That is what most new locks require. The easy way to do this is with a hole saw. The hard part is keeping it centered over an existing hole without running all over the door. My old trick is to first drill a hole in a piece of plywood or paneling. Then clamp the plywood over the old hole at the correct position. The plywood will keep the hole-saw centered and not run all over the door.
That was my old trick. We now have a door-drilling jig with the backset built in. No measuring, no deciphering, just clamp and drill. Most hardware stores and lock shops rent them for a small nominal fee.
Once drilled, attach the doorplate, the backset, and then the knobs. No gluing, no wood putty, no waiting.