Really?
I've never heard of having to swap the leadscrew to cut any thread, whether a right-hand one needing a 3-step gearing, or to cut a left-hand thread from 1 and 2 step gear-trains.
The reversal is normally by a tumbler-gear between the spindle pinion and the first stud wheel.
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If your lathe can take only a one or two stage change-wheel set anyway, then the problem does not arise:
1 Step: Spindle Clockwise (looking on end of spindle) – Idler (anticlockwise) -Leadscrew (clockwise)
2 Step: same but the idler is replaced by two wheels keyed together, and the leadscrew wheel is moved outwards to meet the 2nd middle wheel.
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On the EW with its standard change-wheels, that will cope with most BSF, BSW, Brass (26tpi) and ME (32 and 40tpi), and most of the smaller-pitch UN series. It won't manage 1/4" and 3/8" BSP threads, at 19tpi, with its standard wheels.
If you want to cut metric threads you can get close to some of the common ISO-M ones with the standard wheels, over short lengths of thread. Otherwise you'd need include a 63T or perhaps 42T wheel if you can obtain or make one of proper form. (The EW won't have room for a 127T wheel but 63 and 42 give close approximations based on 63 X 2 and 42 X 3 each = 126.)
The least accurate ISO-M thread it can cut is M8 X 1.25mm, giving an accumulated error of 0.32mm short on 10 turns. (30T spindle, 40+35 stud pair, 65 lead-screw).
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NB: Don't try to cut threads approaching or exceeding the lead-screw's own 1/8" lead. It is unfair to most lathes, usually needs operating it manually from a leadscrew hand-wheel; and is certainly cruel to a small machine like the EW.
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3 Step (.e.g Myford and most lathes with change-wheels and 8 or 4 TPI leadscrew): then by tracing the rotations along the wheel chart rows shows where you use the tumbler reverse.
To emulate that on an EW Stringer lathe would not be easy but since you'd need make a 2-stud banjo anyway, that could be designed to take a reversing wheel.
I think this is more or less how the Drummond B-type lathe reverses its leadscrew. It has no built-in tumbler, as on the Myford 7, but its headstock has a pair of slotted lugs, like ears, to take the reverser pinion stud.