Disclaimer: Use what I state here as "educated opinion" and NOT AS PROFESSIONAL ADVICE.
If you have a 2HP lathe, that's about 1500 W at the shaft. Accounting for inefficiencies, that's more like 2000 W electric.
1 W is not equal to 1 VA (power factor, which we will minimally discuss). But for rules of thumbs, with a good modern controller that uses vector control (don't ask, seriously), the vector drive looks very much like a resistive load (like an incandescent bulb) to the power line, in other words, a power factor close to 1. Older drives will have a power factor much less than 1. As a rule of thumb, at a power factor of 0.5, 1 W requires 2 VA.
It is very likely that your lathe will not show a power factor number anywhere, but you can make a good guess based on the voltage and current rating of the lathe on a plate stamped near the motor or controller.
I suspect that the Robust AB uses a (purchased) vector drive; ditto Powermatics. I would look at the lathe's electrical rating plate, which will list maximum current draw. Multiply that by the voltage rating to get a VA number (e.g. if the lathe says 10A, 220V, 10x220=2200 VA, so you need a transformer good for 2.2 kVA. Don't get the 2 kVA, go next size up, which is likely 2.5 kVA). The 10A is a peak value--the lathe won't be drawing 10A most of the time--only during times of high power (accelerating a large rotating mass, etc.).
Almost finally: If your lathe is (using my example) a 2HP lathe, with 10A/220V on the plate, that means that effectively, you should connect to a 20A circuit at 110V (practically the same VA at 110V or 220V). Most household circuits are 15A (the outlets, anyway, even if the circuit breaker in the panel is 20A). Some outlet receptacles may not be compatible with a 20A plug (1 horizontal blade, 1 vertical blade, round prong).
A 2 or 3 kVA step up transformer runs roughly $200 to $300. I bet that if you have your house's electrical panel in the garage, an electrician could wire up a 220V outlet from your electrical panel (if there's physical room in the panel) for 2 hrs of labor + parts.
Your house also almost certainly has a 220V outlet in the laundry room. Think about just putting the lathe in the laundry room, and doing away with the clothes dryer--after all, what's more important? Dry clothes, or turning happiness?
Best,
Hy