Unless you're going to replace the V-belt with a toothed belt, running the motor closed loop will be of no benefit.

I can't remember the exact details, but essentially sensorless vector drive measures the motor back EMF to determine how it is, or isn't, moving. It's essentially a very complex open loop drive that is able to drive motors very slowly and smoothly.
A full closed loop drive, will most likely use very similar technology, however it allows the connection of an encoder so the drive knows exactly where the motor is.

In terms of a lathe spindle, the most important thing is whatever controller you're using gets a suitable signal from the spindle. Unless you're planning on doing something that involves really accurate spindle control like rigid tapping, the only main requirement is a well controlled and steady spindle speed.