Patio Door Lock

I'm not sure exactly what you have, since I can't see the entire handle set, but consider our 82-044 outside pull and 82-315 key lock. Assuming your handle's hole spacing is 3-15/16", this could be a good solution.

Keep in mind the markings you're showing in your photo don't tell us anything. My suggestion is an educated guess based on what I can see of your handle.