Use thread gauges to check that the thread angle and pitch conform to the drawing above.
Not knowing the lathe, guess that it is quite a few years old, and if of British manufacture, would expect the thread form to be Whitworth.
Assuming the aim is to produce a backplate , or catch plate to screw onto the sapindle, the most likely option will be to screwcut the thread. Thread depth will be 0.0534″
Tracy Tools do not show a 1 x 12 tpi Tap in their ncatalogue (It would take a lot of torque to drive one anyway.
You could rough it it out and then finish it with a thread chaser, or a single cutter from a Die Head, (In a 0.8932″ bore there may be enough room for a single single Die Head cutter).
You could make a plug gauge to check the internal thread, using the thread on an existing backplate as a gauge to check the thread on your plug gauge, as you make it.
The item will be located by the 1.000″ register, so the thread is to pull it into place, so ABSOLUTE precision of the thread is less vital. Once in place, on the spindle, the final machining of the OD and the face and register for the chuck can then be done to maximise concentricity.
Howard