What are the fundamental parameter by which lubricants are graded?
Lubricants are usually graded for a host of different properties, but ultimately what you are looking for is it's thermal stability, and a viscosity index related to the temperature your mills parts run at. These properties are optimized for different parts of the machine because they run at different speeds and as a consequence temperatures. I could delve into more, but I would need more specifics about the machine itself. If you wish to pursue the problem further on your own I would suggest This website as a reference. Also take a look at this cautionary article regarding accurate measurements on viscosity index as it can be a bit tricky. 

The consequence of using the wrong lubricants varies based on how wrong you are... But ultimately the lubricant will thin out to the point that is does not decrease friction and or cool the parts it is lubricating if it degrades at the temperature the part runs at.