Yes, the coolant pump is 3 phase, 1/8 hp. Its function is optional as I usually cut dry. I might even go with a coarse misting system and Kool Mist. This lathe has so much more capacity than my other one that everything changes.
My best understanding is that if there are multiple motors, they all have to be started at the same time and that is apparently OK. Turning a motor off and on while another is running can damage the VFD. My space is very limited so a rotary converter would be difficult to accommodate.