My lathe didn't come with a coolant pump. It's prewired for a 3 phase one though. I have a stand alone coolant pump that's 120V that I can wire in if I choose to use it.
I got a deal back in 2004, Grizzly tools, had a super deal, never was in the catalog, online lathes for sale. I paid $7500 for a 18x40 (450x1000mm) lathe, 5600lbs, that has a 3-1/8" hole through the head stock (listed as 80mm outside of Grizzly's spec's. I wanted a large hole for shaft work, as part of my hobby is fix of broken stuff, and the 10x24 Jet lathe I got in 1976 was too small.
So what I found under the grizzly slapped on label was some other fake importer tool company, that had no searchable existence in the world. And from talking to Grizzly's customer support, as my #4MT tail stock had a manufacturing defect that prevented tool insertion past where they cross machined the taper push out hole in the quill. So they sent me one from their parts machine. The lathe was shipped out of MO, but parts was from their East coast store (now gone), and their customer support machinist (a real smart old retired guy that worked for them) indicated they had 6 of my size lathes and some others that were the 60 and 80 inch (1.5, 2 meter I'm trying to do this metric stuff) beds of the same import quality. They are good quality, except these are every incorrectly made part or spare excess parts put into assemblies at what was a big discount as scrap iron cost's to the importer. And I was seeing lathes from Grizzly of this same size in the $16K+, and Enco was $20K. I wanted it, and I'm happy with it.
So I did to through and kept the original safety interlock relays in place. I just pulled the old 3 phase power from the one contact I reused in each of the FWD/REV contactor motor switches, as there were no spare Aux contacts.
I did try to power it with my RPC of my build, and it caused some sort of high voltage arc to occur, and short out the FWD motor contactor to have a phase to phase short. I could not find where it was, but Grizzly sent me a new contactor from their spare parts machine. But to power 7.5HP main motor, I needed something to not deal with the locked rotor amps of startup, that would exist with 3phase line input, and my RPC could not deal with that.
So I got a 10HP Mitsubishi VFD (typical derating of the VFD for motor HP >3 is 2X VFD size to prevent input diode smoke release) that I integrated into the controls. I've never had an issue with the 30amp one phase input, it's never tripped the main breaker. More issues with tuning the deceleration so it does not overvoltage or trip some internal overcurrent brake resistor. It's of the same age 2004 (the VFD), and if it were not such a large size, I would get a replacement. I don't trust China low cost ones, but I may be wrong in them, as they've only learned how to make everything better and cheaper, especially since all US and EU name brand VFD's are made in China. Also I'm seeing them selling on eBay VFD for single phase input, to drive 40HP motors.
What they need is a VFD, that senses the motor load, and decelerates to stop as fast as possible. It would get the inertial data from monitoring the acceleration of the lathe chuck and part. It's just a hobby, not production, but safety is why I want fast deceleration. And if the VFD trips out, not helping.
The VFD on the lathe allows you to slow it down for die or tap threading to keep it under control (you're holding the wrench), and this as well slowing it down when there's harmonic noise in the cut.
I kept the main power switch of my big lathe. I know all these lathes with apron control FWD/REV levers, have similar contactor arrangements to interlock the motor from powering up, in the event of power loss, as well if there are door switches and such to lock out operation for the guy that wants to get his fingers crushed on purpose.
Since you have the diagram, the change is simple. Just keep the low DC signal stuff from any accidental AC mains power. The VFD manual has all the good install advise. The EMI is BS if you don't have long runs of motor wires. That's all industrial where motors are remote to the main VFD and contactor control room, that can be 1000s of feet away (as dumb as as this, but I worked on grain elevator in my youth as a apprentice, 300-500ft tall) and they had a remote lockout switch, that was two #14AWG copper runs per motor up in the head house, for electrical lockout safety of a maintenance guy that removed the covers to the motor belts and such) my point is that's when you need EMI/EMC filters and stuff. But on 10foot (3m) runs the switching noise has never gotten into the unshielded analog and discrete connections on any of my machines. My metal shop, all motors are 3 phase and for the drill press and old lathe, they got 3phase motor conversions a long time ago. I don't mess with belt changes unless I need some real torque, otherwise the mid range, and let the motor spin up to 120Hz input max to get the upper range of the spindle.