Hi
It would be helpfull if you could post a link to your manual, so that more knowledgable members than myself might be able to help.
I replaced the single phase motor on my lathe with a reasonable cheap VFD off Aliexpress and with the help of a c ouple of members on the forum i managed to get it sorted.
On my unit there was a terminal on the bottom of the VFD with 5V supply that let you control the motor with via a low voltage with a variable resistor for speed control, i had a requirement for reverse so included a 3 position switch.
Just work your way through the manual and you should be fine.
Regards
Mike