VFD

I previously stated VFDs generally don't do well above 3HP... I should have specified VFDs don't do well generating the third leg of three phase power above 3HP... They are great for speed control.... I've worked with AB stuff in plants, definitely better equipment but it comes with a much higher price....
This is a bit incorrect, a VFD doesn't generate the third leg. A rotary phase converter generates the third leg. A VFD is typically a two part machine in that it has on the input side a Converter front end that typically uses diode bridges to convert AC to DC voltage and Bus capacitors are used to smooth the DC and eliminate AC ripple. The output side is an Inverter uses some sort of silicon transistor, FET, MOSFET, or IGBT arrangement to convert the DC back to AC at the desired RMS frequency. That frequency along with the motor pole count is what determines how fast the motor spins. 230V VFDs that have single phase inputs can have limitations as to how large a motor can be driven, and that is determined by the size of the converter used in the front end. You need a significantly larger single phase converter section to be able to handle the same current that a three phase bridge can. Three phase input VFDs don't have this limitation, but typically aren't useful to home shop types that are looking for the single phase 230V input aspect.

I can go on and on an on about this VFD control theory topic but won't bore you. I am an engineer for AB in the facility where all of the low-voltage (600VAC and down) VFDs are designed and some of the mid-size drives (50-500hp) are built. I actually work in the motion control Servo business, which is essentially a VFD with a dedicated position feedback input for use with permanent magnet motors in robots and repetitive motion applications like packaging.

Just curious what voltage those are running on. The biggest I've been around have been 250hp on 480 and that pair with power filters took up a 12 feet of wall space.
We have a Medium-Voltage division that handles drives from 600 - 11,000 volts, with the more common ones being 4160VAC. Those drives essentially fill a room and the motors can be more than 32,000 HP. There are a lot of MV motors around 500 hp too, because the higher voltage allows use of much smaller conductors, and copper costs often drive the decision.
I need VFD for my lathe. I’m looking at a 3 HP 10A model. Is that going to be enough for a 2 HP lathe as far as the amps go?
The simple answer is yes. You can use it as a speed controller as well, but don't expect to get any decent torque from a low cost simple VFD and regular induction motor, much below the 40Hz range. Below that the torque suffers and you need more advanced loop control, as well as an auxilliary cooling fan to prevent burning the motor insulation. Still better than nothing, but you will need to use the mechanical speed control in the head for large speed changes.