If it has a controller, I'm guessing you're looking at a CNC machine, not a manual lathe, but you should clarify that. So it will be the servo power supply(s) that run on 480VAC. Many of the CNC controllers run on 120VAC with their own internal power supply (basically an industrial PC). You should not need to use a transformer to see if the controller will boot.
I just found a manual for the Fagor 800T stating it needs to connected via an "...independent 110VA shielded transformer with an output voltage between 100VAC and 240VAC." For testing purposes a 120 VAC plug in to home power should suffice, shielding would be critical only when the servos are active. If you look in the control cabinet you can probably find the controller, and it may have a power cord going into the controller with the classic three prong interface, google
IEC-320 for pictures. Editted to add: Page 12 (36th pdf page) of this
pdf version of the 800T controller manuall shows the pwer input in the upper left area of the controller back panel. It also shows the location of the lithium RAM backup battery.
If it boots, it'll probably still alarm since nothing else has power, but that would give you a go/no-go on the controller. If it doesn't boot it may just be the "CMOS" clock battery that holds the boot params, which probably can be restored with the help of someone with some PC tech skills. (
I'm not positive that the Fagor controllers are PC based, but it is possible) Just don't do something that erases the hard disk as likely re-acquiring the right OS, and control software, with licenses, would be prohibitive. Again, someone with skills in that area can help you make a copy of the hard disk before even trying anything else. I do that with Linux using the dd command personally, but there are a lot of ways to go about it.
I'm playing with slowly rebuilding a CNC mill (VMC) to run on a new controller. May never get done, like several projects I have, but it keeps me entertained.