That lathe's been modified to take a Vee-belt by fitting a pulley to the original flat-belt one, and making a countershaft.
Machine-tools like that were made for driving from overhead line-shafts, and the belts were cut to length from stock material, threaded round the pulleys and joined with clips.
That Vee-pulley may be hiding a grub-screw or two in the original pulley: I am guessing it is fitted by screws to one of the original pulley steps.
Or as Dave says, use link belting. In which case just cut the existing belt!
I'd be inclined to reverse the order there, too. Use a full Vee-belt on the intermediate drive and link-belt from the countershaft to the spindle. I can't tell from the photographs how the intermediate belt is tensioned, but one option would be spacer-plates slotted for the bolts, between the pillow-blocks and the frame.
Incidentally, having owned an IXL-badged lathe in the past, those initials seem to have been of a dealership or badge-manufacturer. Examining the photographs on lathes.co, I think the actual maker was a German company called Ehrlich.