Just to correct this slightly, as I feel it's a bit misleading.Electric motors are designed to have peak torque at their rated frequency, significantly higher or lower will reduce the available torque and increase the temperature of the motor with a constant load. Not really a consideration with something like a pillar drill that has lots of on/off cycles but a lathe can be run for some time. Personally, I'd look to use the gearing more and use a VFD to fine tune the speed.
A motor will produce peak power at it's rated speed, which for UK/EU spec will normally be at 50Hz, with the actual speed depending on the number of poles (at 50Hz, divide 6000 by the number of poles for the rough speed. Actual speed will be very slightly lower due to slippage, but near enough not to worry about in most applications).
Below the rated speed, the motor acts like a constant torque source, so as speed drops, so does available power.
Above the rated speed, the motor acts like a constant power source, so as speed increases, torque decreases.
The biggest issue is when running at lower speeds, motor cooling can become an issue, but can easily be fixed with forced cooling.
There is also the issue that at very low speeds, in that motor cogging becomes noticeable, as the rotor essentially starts to noticeably spring/jump between poles, as the switching frequency is lower than what the inertia of the rotor can damp/smooth out.
I mention that last bit, because this is why I would personally recommend sticking with a 3 phase motor.
It's very common for single phase driven machines to have imperfections in the cut due to 50Hz surges the motor experiences. A 3 phase motor's rotor is continually being pushed/pulled by the 3 phases 120deg apart, whereas a single phase motor's rotor is continually being pushed/pulled by just the one 50Hz phase, and relies heavily on the weight of the rotor to smooth those surges out.
Plus with a VFD driven 3 phase, it's far quicker to adjust speed, but on a gearhead lathe, that's not quite as big a benefit as on a lathe that needs belts changed for speed changes.