door lock for a K0039 sliding glass patio door

Hello! Looks like you're showing us the mortise lock for your door. If that's all you need, then I recommend our 82-226. If you look over our pictures and dimensions, I feel confident that you'll agree this matches your hardware very closely.

I'm not sure if you also need the handle set, but if you did then I'd recommend our 82-086. This is also very similar to the hardware I see in your photos and I think it's worth looking over. Otherwise, the 82-226 should be fully compatible with your old handle set. If that's still in good condition then there's no reason to replace it.

Please let me know if you had any questions, I'm happy to clarify on any point you need.