Would you start allopurinol for a patient with uric acid kidney stones who does not have hyperuricemia or hyperuricosuria?

Definitely not! The main risk factor for uric acid kidney stones is neither hyperuricemia nor hyperuricosuria; it is hyperaciduria. Typically uric acid stone formers have a urine pH below 5.8. Raising urine pH into the mid 6s will not only stop new stone formation and existing stone growth; it will typically dissolve uric acid stones! The most common cause of excessive urine acidity is type 2 diabetes. They lose the ability to convert urinary ammonia (NH3), which is neutral, to ammonium (NH4), w...

I do not start allopurinol or other uric acid-lowering therapies in the absence of hyperuricemia. The most likely cause of the uric acid stones is aciduria, which I would treat with dietary changes, possibly with citrate or bicarbonate, as we would want the urine pH to be between 6.0 and 6.5.