When replacing the thread in the half nut you might run into a problem with the lead screw its self. On most lathes we use the section up close to the head stock the most. The most wear on lead screw will be on the head stock end of the screw which changes the pitch of the thread, so new threads in half nut will fit the tailstock end of the screw very well but will be lose on the worn portion.
Years back we use to take the half nuts out of the carriage and apron and machine the center section out and then set up on the tail stock end of the lead screw and pour Babbitt to replace the cast iron that we removed, it worked great made a great thread. :thumbup: