I take it you have the LNS Manual and the SMEC one.
Dig thru your SMEC electrical manual or Ladder Manual if separate, and find where it lists the X inputs and Y outputs. These are going to be the wires that talk back and forth to the LNS. (Along with basic AC power input to the LNS.)
The Y addresses will be the lathe telling the LNS what to do. The X addresses will be how/where the LNS tells the lathe that it's followed orders. (Also connections for E-Stop and End Of Bar etc) With careful enough attention to details in the manual, besides spelling out the function, it might show connection numbers, terminal strip numbers, connector pin numbers, wire numbers. You just never know how thorough MTB's will be with the manuals. Could get lucky and figure it out on your own. Of course that depends on how much time you have.
I'm surprised if the LNS manual didn't have the pinout in the manual. I'm sure LNS would.