Lock from door handle broke off

Is this handle's hole spacing 4-15/16", from center-to-center? If so, you might be able to use our 82-240 thumb latch, but it may not work with your older handle set design. If the hole spacing is indeed 4-15/16", see the 82-080 or keyed 82-081. I am afraid these do not come in black finishes. Apologies for any inconvenience. 

Finally, please note that damage like this to the thumb lever may be indicative of a mortise lock that is broken and should be replaced. To find out, remove your handle set and try manually flipping the lock with a slotted screwdriver. If it doesn't budge, it is broken and you'll need a new one. See if either the 82-238 or 82-268B matches what you have.