Spindle lube malfunction has nothing to do with the spindle coolant chiller.... But while you are at it, clean the air filters on that too, and the coils
if they are nasty or it will throw you an error.
The last Mazak mill I got to play with, we had the spindle coolant, some oddball funny smelling stuff (vactra #3???). The way lube, which used waylube, and the spindle
lube which was some ISO 36 (? maybe, its been a while) hydraulic oil. Looked almost like the waylube pump, had to fill it every so often or we got an error.
Is it full?, if it is, is the internal filter clogged? If not, you are looking at either a high pressure (not oiling, clogged injectors) or a low pressure (leaking) problem.
Shouldn't be that hard to track down.