It seems there is a magic lubricant and coolant for every everyone! One might ask what are the scientific purpose of these ... from a physics stand point. My perspective is that the main reason for using these is to protect and extend tool life, but since the work piece gets hot and this heat also transferred to the tool cutting edge.
So for me the lubricant is to help to keep the work material from sticking to (transferring to) the tool, or reverse, and more importantly to reduce the friction between tool and work when the tool is not cutting but just rubbing. Coolant is just that, keep everything cooler so there is less wear. It is obvious that if a cutting tool gets hot enough the surface can approach the melting point, but even just a little heat tends to soften the tool surface resulting in removing layers and destroying the sharpness. The best coolant is one which has a large heat latency as oppose to just having a heat capacity. Water would be great if it does not cause rust. This is because it takes the heat of latency to go through 100C temperature point and evaporate (boil) away. The best part of water it is human compatible (non-toxic), where as some of the expensive coolant/lubricants you can buy causes a vapor (choking smoke) that will drive you right out of the room. However, they too seem to be built around having a heat of latency not just heat capacity.
Years ago I learned of a manufacturing process used to mold certain glass materials to final shape using Carbide molds. A piece of glass of the correct volume was inserted into the mold, the materials were heated until the glass was soft and then pressure was applied to form the final shape. This worked fine a few times and then the glass would react with the SiC mold surface and would stick to the surface. Removing it left the mold surface with pullouts and the sticking got worst. So the expensive molds did not last long! So naturally, folks started applying lubricants to try to prevent this. Since nothing worked very well, desperation drove some workers to even try the greasy surfaces that were in the lunch box! The cheese wrappers worked a little, but so did nose oil! (I am not recommending that you rub your cutting tools on your nose!
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In the end, the solution was to remove the Oxygen from the system and to use no lubricants or other contaminates! The molds and glass were evacuated, back flushed with Nitrogen, until the Oxygen was removed from the volume and surfaces and then the hot surfaces, and then the pressure was applied. The volume and surfaces were cooled with Nitrogen, and then the molded glass could be easily removed. This became a manufacturing process where the molds lasted for thousands of times.
So it probably makes sense that oxidation could also play a role in tool wear in the cutting process. Likewise, hardness and toughness are important, but the melting temperature difference between material to be cut and the cutter material plays a big role in how long the cutting edge will last.