Most Monarch lathes have the actual machine weight on the data plate.
A 10EE has a 5HP motor. I think that lathe has a relatively low top spindle speed, less than 1000 RPM, so 10 to 15 HP is probably in the ballpark.
I imagine the motor is wired
There are plenty of VFDs up to atl least 30HP that can be single-phased. Some mfrs don't say so unless you ask -- Yaskawa is one that does specify in their literature which drives will operate on single phase.
It's not so much the expense of the box that
For the stuff I do the low spindle speed would be a problem, you should evaluate whether you can live with it.
You'd have to look at the motor and determine whether it's a proprietary mount.