Legacy door lock
We sell a handle set that matches your original, yes. See our 82-086. However, I'm a little confused by how it actually locks the door. Your door doesn't have an opening for a mortise that the 82-086 is designed to work with. It's way, way too small.
Was this door repaired at any point in the past? If so, I believed they used the wrong parts. We don't sell a mortise lock that works with the 82-086 that would also fit in your door.
Okay, seeing the keeper is a big help. That'd be our 89-027. This is used with an entirely different handle/lock system than what you have on the door now. Somebody definitely repaired it at some point in the past, and they repaired it incorrectly.
I recommend using the 82-003. This has a 3-15/16" hole spacing, which should match the holes in your door now, and is actually made to work with this keeper. Give it a look and let me know if you have any questions.