I would like to add a lock to this

Thanks for writing in. Installing a key lock to the outside pull is pretty tricky for this type of handle sets; we do carry key cylinders that technically are compatible, but you'd have to file a hole just right to snugly get the key cylinder into the outside pull. It is honestly a safer route to just go with a new, keyed handle set. See our 82-081. Go over the dimensions to ensure this matches what you need.