Door lock key

This looks like an 82-086 Handle Set. You can replace the internal key lock with our 82-310. This blog article here goes into some detail. Note that you might want to check if the mortise lock in the door isn't broken. To do this, remove the handle set and try manually throwing the lock with a flathead screwdriver. If it doesn't budge, the mortise lock should be replaced as well. Show us a picture and we'll see if we can provide a new one for you.