We can speculate or discuss the finer points of the fan fitted to Blowlamp's motor but its an irrelevance to the original topic.
The motor itself, or rather the use of a 'sewing machine' motor is very relevant to driving a lathe. I have only done a small amount of Googling since I saw Blowlamp' picture but it seems to me that these motors could be game changer for driving much of our smaller workshop machines.
These sewing machine motors are no different in principle to other brushless motors but I suspect the sewing machine market is quite large so pricing and specification is quite good. They seem to be sold complete with driver and accessories to allow retro fitting by non engineering customers. Most are complete with a linkage to a foot deal to vary speed. Some are described as 'servo' motors which means that even if its not a true, all singing all dancing precision servo, it will be very controllable (good for tapping, screwcutting etc).
The one in blowlamps picture appears to have a ribbon cable between the motor and controller (so not very robust) but others I found in searches have better cables and connectors. I'm tempted to buy one just to experiment and fit to an X1 type mill I have that is just sitting around.
Ian P