faucets. handles

I just disassembled my faucet (which is pictured below), and I have a hard time putting it back together... No matter how much I tighten the mounting nut, it always comes loose again once I close the handle. (You turn the handle left to close, but this will loosen the nut.) Is there some trick...

Health Dept has told me I cannot reopen my cafe until all my faucets handles are changed to 4" wrist lever handles. My produce sink and hand sink have different handles, but they seem to be interchangeable. The first photos are of those two sinks and the two styles of handle. The faucets on...