I had a similar question come up with another poster from Australia. My understanding is that the the standard voltage in Australia, NZ and UK is single phase 240 volts at 50 hertz. Standard electric motors in industry use three phase, ~415 volts at 50 hertz. VFDs are usually rated for an input range and an output range. So you will often see VFDs rated for 200-240VAC or 400-480VAC inputs, so there should not be a problem there. There are a few smaller VFDs that can step up voltages, but normally this is for the 100-120VAC single phase to 3 phase 200-240VAC and for small Hp motors . There are very few VFDs that will step up the voltage from and input of 240VAC. So for a 415VAC motor you would most likely need to use a 3 phase input VFD to output a similar 3 phase voltage. Your VFD base speed frequency setting would be 50Hz (motor name plate). Link below are some unique VFDs that convert 240 to 415VAC, FYI.
http://www.drivesdirect.co.uk/Products/Digital_Inverters240_415.htm
http://www.drivesdirect.co.uk/how_to_choose.htm
Next would be the motor, so you would need to match the motor voltage to the VFD output, I assuming the replacement three phase motor would be 415VAC. There would be a benefit of up sizing the motor to 2 Hp, as Hp falls off in a linear fashion below the base speed, torque usually remains flat down to almost 0 Hz depending on the VFD and the motor. You may be able to source a 3 phase 240VAC motor and then run this off of a single phase 240VAC to 3 phase 240VAC output VFD. VFDs also have the ability to boost a motors output rating for short periods (up to 1 minute), so unless you require the full Hp continuously, the VFD can compensate to some degree for the decreased Hp below the motors rated base speed.
Newer motors usually have better insulation many of them have inverter rated wire insulation, so less likely to have insulation breakdown issues. This issues almost never occur in 3 phase motors that have dual voltage ratings and are run at the lower rating of the two operating voltages. Motors run at the higher voltage of 400-480VAC would be expected to be more susceptible to long term insulation damage with a VFD if the insulation did not have a inverter rating. As mentioned, many newer motors have better insulation, but if it is some generic low quality motor than I would be a bit more concerned. As far as speed range and cooling issues of motors run outside their nameplate specifications, most 3 phase motors do fine running them off a VFD in a range of 0.5-1.5 times their nameplate rated RPM, and most 1550-1750 RPM motors designed for 50-60 Hz should be able to operate up to 100Hz, although I would probably choose something like 80-90Hz. Cooling issues could occur above this range, and Hp/Torque can also fall off faster than expected. Cooling issues normally are not an issue with a TEFC motor unless operated continuously under heavy load at speeds under ~20Hz. There is normally no "derating" as such, other than Hp is less below the motor designed base speed, so a 2Hp motor at say 50Hz, would be 1 Hp at 25Hz. It is common practice to uprate a 3 phase motor if it is going to be used under a very wide operating range (5-10X), and/or there is a minimal required Hp/Torque needed at specified operating points.
So you do not need a special motor in this application, but there are motors that are called inverter or vector motors that are specifically designed to be operated with a VFD over a very broad speed range. These are very expensive, you would do fine with a the standard 2 Hp mentioned, you should be ok to operate it in the 25-100Hz range. The other factor that has not been addressed is the nature of how one usually controls the VFD operations and how they will work with your lathe. Almost all newer three phase lathes, use contactors and a power relay to prevent auto start, and often have interlocks. If the VFD controls are wired directly to the spindle switch this can lead to safety issues, so how the VFD will be wired into the lathe is a concern.
Another simple alternative to consider might be to go from a single pulley drive to a dual pulley with 2 ratios.