Converting the lathe to 12VDC could be done, with a winch motor. The ones from HF have a magnet as the field.
Relative speed consistancy. It would involve a (relatively)
permanant conversion to the machine. As such, I would advise against it. It would work, I have such equipment as a "worst case standby" for my own shop. One of those "Just In Case" scenarios. But I don't expect to use it. The GenSet on my tractor PTO is my primary standby, seven KW for as long as the diesel lasts. I have a couple of 55 gallon drums.... BTW, my residence is about two KW total. I don't use air conditioning or electric heat.
An automotive starter would work, worst case. But not very stable, it is usually a series wound motor. Good for hoisting but not so for speed stability. Should you use such an option, be sure to provide for cooling. Such motors are not set up for continuous use.
An inverter is the second best option. It would involve some really serious batteries, a
lot of them. And solar or wind power would take a serious plant. Not something I would want on a vacation property. The consideration here is wattage. Figure one KW continuous. As in, more than ten minutes. That would take a
lot of recovery time.
To my thinking, a small genset would be
first choice. A small plant that could be picked up and carried easily. Easier than the machine. One to several
hours run time. There are smaller plants than one KW, 1000 watts. But for continuous use, one KW would be the minimum. No, the lathe doesn't pull that much, except when starting. For field use though, several starting cycles is a good idea.
The other option, which I gather is not usable in your case, is a belt from the PTO of a Japanese or Chinese tractor. The kind with a multi-speed output. Many small American tractors are made overseas and have that option.
The bottom line here is not power but storage conditions. If the machine is to be left at a remote location, it must have regular maintenance so it doesn't rust. Even a light surface rust would ruin the accuracy of the machine. If it is to be transported to and from, consideration must be given to alignment. Again, the bottom line, storage. If it to be carried out for a week-end, why bother. For longer terms, a genset is a must.
Just my opinion, of course;
Bill Hudson