One can use certain gear ratios (100:127 is the ideal, smaller ones come close) to provide a conversion between metric and imperial threads.
*But* -- during most threading, it is common to use half-nuts in the apron -- engage them to start cutting the thread, disengage and quickly crank the carriage back with the large handwheel, then re-engage to cut the next pass of the thread.However -- there are multiple points at which the half-nuts can be closed, and only some of those will retrace the previous cut (which you want to do -- only deeper). For this, there is usually a "threading dial", usually on the right side of the carriage, though I have seen them built into the apron and flush with the top of the carriage.
Anyway -- the dial tells you when to close the half nuts to retrace the same thread path.
On imperial lathes with an imperal leadscrew, this works only with imperial threads.
On metric lathes with a metric leadscrew the threading dial needs to have a selection of (typically) four different gears to engage the leadscrew to deal with the different ratios which metric threads require.
In either case, you *can't* use a threading dial for an imperal leadscrew to cut metric threads -- even with the 100:127 transposing gears.
And -- you can't use a threading dial for a metric leadscrew to cut imperial threads even with the 100:127 transposing gears.
So -- the only way to cut threads on the other system (unless you are cutting a fine enough and shallow enough thread so you can cut it in one pass) is to halt the spindle before you reach the end of the thread, perhaps use a hand crank locked into the spindle, to crank the rest of the way to the end of the thread, back the tool out of the thread, crank in reverse to the starting end, crank the tool back in with the extra depth for the next pass, again use the power for a long thread but being sure to stop it before you reach the end, and crank again and again.
So -- you *can* cut metric threads on an imperial lathe or vice versa with the transposing gears -- but is is a royal plain. So modify the statement to read "You can't *conveniently* cut X threads on a Y lathe" and it becomes true.
The only exception to this is on CNC lathes, where there is no direct gear connection between the leadscrew and the spindle. Instead, the spindle has an encoder which gives one index pulse per revolution, plus a lot of incremental pulses ever few degrees. The computer handles turning the leadscrew the right amount for each incremental pulse to cut the threads. The computer then backs the tool out at the end of the thread, and reverses rapidly to reach the starting point, and then waits for the next index pulse to start the same thread pass again -- deeper. So -- it is a mater of telling the computer whether you want to work in mm or inches. (Oh yes -- and learning to program the computer. :-)
I hope that this helps. It would have been easier if you had already had the practice of cutting threads on a manual lathe of one system or the other, so you would know what you would be missing.
Enjoy, DoN.