That requires expensive and precise tools outside of your price range including a torque wrench and dial indicator with base. You need to swap the ring gear and re-set the backlash and contact pattern with the pinion gear. This is a time consuming and ardious task for a do-it-yourselfer. You'll also need a press to get the carrier bearings on and off.
The detroit has its own carrier built in, the ring gear bolts to it. The lockright is a "lunchbox locker". It fits inside the standard carrier where the spider gears are and is driven by the cross shaft. The ring gear bolts to the carrier. Since the carrier and ring gear don't need to be removed to install the lockright and other style lockers, you don't need the special tools or talent to install them.