Door lock and handle needed

We carry a ton of handles with a 3-15/16" hole spacing, but the cutouts in your door are very peculiar. I don't think any of our handles in that size will work. 

You may want to opt for one of our surface-mount handle sets. These are nice because they don't require any internal hardware to work, allowing them to work on just about anything. The issue is that few of our surface-mounts have a 3-15/16" hole spacing. 

Consider our 82-261. This may work well for your door, but look it over and let me know if you agree. We also have an unkeyed version, the 82-261B, and a version that lacks the mounting plates, 82-261C. Based on the cutout in your door though I think you'll want the plates.

The plates in question just go under the handle. It gives it a little something extra to sit on, and in your case they'd be beneficial since they'd cover that big rectangular hole in your second photo.