I keep a large UPS around to plug my electronics into when I need to run them from the generator I have. Spikes and line noise are the most typical issues with generator electricity. It looks like your lathe has a 3 phase inverter built in. I'm not sure how many amps/watts your lathe takes, but I assume 15 - 20, which would require a pretty large/weighty UPS.
A of it depends on the quality of the signal coming from your generator. You'd need to find someone with an oscilloscope to "listen" to the signal and see what it's generating. The person running the oscilloscope will know what you need to look for (spike, type of signal). The more high end generators typically have better conditioning circuits to create cleaner electricity for home electronics. I'm sure there are some reviews of this on the interwebs, but I haven't searched for any.
You may be able to get a line conditioner as well, but haven't searched for those either.
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