Door handle with 2 screws on side.

Your patio door handles remind me of the 82-080 Mortise Style Handle Set. The keyed version is the 82-081. I confident this should be a match but to confirm that this is the right replacement be sure to double check the dimensions.

The mortise lock, sold separately, appears to be the 82-238 Double Hook Mortise Lock. The specifications for it can be found directly on the website.

Dimensions for 82-081