How many horsepower are you trying to drive?
Are you going to push the machine to this max horsepower.
I have to assume you can wire the motor for 240VAC 3PH. If your not pushing too much over 5HP, you can do this with single phase 240VAC, and use a VFD (generally over 3HP you need to use a larger then needed VFD and derate, ~60-70% of VFD).
I looked at Hardinge HLV-H and looks like a 11"x18" lathe, this should not be more then 3HP, but I'm guessing. My 12"x24" lathe is 1HP, my 18"x40" lathe is 7.5HP.
But if you really need lots of 3PH power, this is a pretty major upgrade to the service. Your local county/city building department (I think this is a state controlled thing in MN, so substitute state for local gov., but I assume a permit is needed), it's getting tough to do electrical work without at least a journeyman's license, and only if the state will inspect this without a Master sign-off. At any rate the monthly meter costs are considerably more for 3PH. And there may be a minimum KW-Hr consumption (you'll pay the minimum at least). But I'm thinking this is more then $3K for starters (assuming you have to hire an electrician).
I would assume if the HP is less then 3HP, the motor would be 240-480VAC, but I know nothing about Hardinge HLV-H. 3PH motors are pretty easy to get off eBay, if voltage was a problem, but then you may need a good drill press or mill to make an adapter plate if you can't find the same NEMA motor frame mount, all depends on how old the machine is. The current standard from my memory goes back to early 60's.
ignator
Also some VFDs designed for 3PH input, require this, and will not operate, so selecting one without this limitation may be important. I'm using a Mitsubishi 10HP VFD on the 7.5HP motor. Their manual will indicate this if you know where to look.