That was my bit of trivia. The belts are laced on each end and held together with a pin. When the tension was released off the drive belt the machinist or operator, whatever the machine happened to be, had a pole with a hook which they could use to slip the belt off the line shaft pulley. They would pull the pin, then twist the belt and pull it around the opposite side of the driven pulley and pin it back together, then slip it back on the line shaft pulley. I can imagine if they were cutting left hand threads they had machines set to do this, because this seems labor intensive. It's interesting to see what happened to get the job done.
Some of the vintage lathes in the transition period to electric motors still used the flat transition belts. My Lodge and Shipley is older so someone fabricated a contraption, of electric motor, large V-belt pulley that that drives the three step cone which acts as the line shaft. The distance between the upper and lower three step cone is only about 30" and it doesn't have enough slack to twist the belt. For it to work (maybe) I would need to get a belt slightly longer just to use for reverse but I'm still not sure if there's sufficient space for the twist.