I need a keyed lock for this sliding door please

Thanks for reaching out to us. Take a look at our 82-310 key cylinder. This should be compatible with your existing hardware, just note that the punchout on your existing handle is centered. Before you buy anything, you should check to make sure that this punchout aligns with the slot in your mortise that takes the key lock. If they're not aligned, it won't work. 

If you need an offset key lock instead, so as to better align with your mortise, then my suggestion would be an all new lockset like our 82-030B. This has a key lock in the exterior pull that can work in either an upper offset or lower offset position.