Jonathan,. This is a metric lathe, ie metric leadscrew, but that doesn't matter. The threads will be approximate but near enough for all practical purposes where it is only a few turns for fixing something. Don't worry about accurate conversions using 127 tooth gears which are not appropriate in this context and on this lathe.
Also you will not be screwcutting under power. Initially you will have to turn the chuck by hand but you should make a mandrel handle (look that up seperately) fairly soon.
You first need to look at the table on the front of the headstock or page 18 – top right section where it says "n/1" " which is number fo turns per inch. Now there isn't an entry for 32 so lets do 16 first of all.
The columns are W, z1, z2, L. W is the mandrel position, L is the leadscrew position.
The numbers in the table are the number of teeth on the gears you will use. The row for 16 colum for W shows 55 so you take off the pulley and the gear from the back of the mandrel and put on the 55 here, making sure not to loose the small 'key' that fits the slot in the gear and mandrel to lock them together. Both pulley and gear may be tight but there are no grub screws to secure them just friction, rust, and old oil goo. The gears in the middle may get in the way so at this stage so loosen the bolts holding the 'banjo' arm they are mounted on and move them out of the way.
Row 16 column L is 40 so you need to put a 40 tooth gear on the end of the leadscrew. I think you can see what needs to be moved for that to happen, starting with the dog clutch assembly. Observe the movement of the dog clutch engagement lever. It moves up to unlock it. You need to set its position so it can move the dog in and out of mesh.
I will continue later but must go out now.