Yes: it forms a two-step train.

The 127 / 120 both fit the middle shaft, keyed together, and the specified order suggests to me the train is 30 -> 127 then 120 -> 48, but you can verify this by calculation.

Still wise to make the first cut just a very light helical scratch you can measure, but not deep enough to spoil the finished thread if it’s not quite right.

I assume the lathe has a thread-indicating dial but you might have to keep the clasp-nuts engaged, stop the machine at the end of the thread, withdraw the tool and reverse the machine to go back for the next cut. That is necessary on many lathes when the cut t.p.i. is not an nice neat integer; as it is not with mm work-piece pitches and inch-based leadscrews.

When cutting metric on the imperial lathe you will need to keep the halfnuts engaged all the time ie wind back by hand or power without disconnecting anything to keep in step.