With an auto or truck you can "double clutch", disengaging the gears, releasing the clutch, changing the input speed with the engine, and then engaging a new gear set at the correct rpm for them to engage smoothly. It can also be done without using the clutch at all. It takes skill to do it without hurting anything. I have driven a manual transmission car home across town with a failed clutch linkage back in the day, using the starter to get moving in low gear and then shifting by matching shaft speeds. It is not really a very good idea, and there is a good chance of damaging or breaking gear teeth and wearing out any synchros or constant mesh dog clutches while doing it. The lathe does not have a throttle pedal to finely control rpm, and so the gears are forced (crashed) into mesh at unequal speeds, which causes wear or damage. If I worked at a machine shop and the foreman told me to do it, I would, but in my own hobby machinist shop on my own lathe where I will have to fix it and pay the cost, I will be stopping the machine before shifting. YMMV.
Higher end lathes probably have constant mesh gears which are more tolerant of shifting on the fly, are designed with that sort of use in mind, and would recommend that type of use in the manual. A real time saver where time means money.