Patio Sliding door lock replacement

It's tough to make out what you have, but I think our 82-002K may be worth considering. Just note its overall size to ensure that it will sit in the space available in your door. Also note that the hook latch is in the lowest possible position it can be, just above the bottom screw. I can't quite tell from your photos where the hook latch is oriented. 

Alternate image for 82-002K

Alternate view of 82-002K Sliding door handle set