So I disassembled the pump last night. Figured I'd put my findings here in case anyone else stumbles upon this in the future.

On the Syntec 4x8 Laguna SmartShop SUV, you can turn the oil lubricator pump on by clicking the "atomization" button on the bottom right of the MAIN panel. I assumed that was for the mister on the machine, they really should have named that better...

You can determine if the pump is on by feeling the pump housing for vibration, or by checking the IO panel, there should be a CNC bits I and CNC bits O page, the O page I believe should have an entry for Nebulizer. When this entry is red, the pump is on. Why this output, and not the one that reads "Oil Pump" right below it? No clue.

Even with the pump on it wasn't pumping very much, there was a ton of air in the lines, and the gauge still read 0. So I took the pump off the machine and took the reservoir off. Hidden by the oil was a kink in the main line on the pump output.

I cut the kinked section out and reinstalled. I took the hose off where it entered the distribution block near the spindle to help bleed the air. I also jury-rigged a cable with what I had on hand to power the pump--it filled up the empty tube in seconds. I have 208Y 3-phase so it was about 215V. For some reason the Laguna only runs 120V to the pump, I'm assuming because they want it to run slower, though it is rated for 200-240V. If I ever have to replace the pump, I'll probably just buy one of those 120V cheap ones off Amazon (just search "oil lubricant pump cnc").

Some info that might be valuable to others. The nylon hose is 6mm OD with 1mm wall, and the fittings are brass compression fittings for 6mm OD. 10mm and 12mm wrenchs for the fittings. I use Vactra #2 ISO VG 68 way lube oil on the Laguna, same thing my Haas Mini Mill uses. Though I think generic 30W oil works too.
Hots were to 1 & 3 on the terminal block, ground is 8.


Anyway, she's working now. Thankfully I hadn't been running it very long before I noticed the air bubbles in the oil lines. I've attached some pictures I took during the process. Hope this helps someone in the future.