The manuals for both of my lathes call for 80-90 gear oil. Most gear oil is non detergent.
If your gear box is clattering/heating then something is wrong.
I like airline/compressor oil for the ways. Not because it's better than way oil, although I don't notice a difference, but it's what I have on hand all the time. It wipes off easily when it gets dirty and doesn't leave any staining.
These machines shouldn't be heating up. There is nothing hooked directly to most of them to generate heat. Some do have large electric motors underneath the gearbox but it should be well ventilated for cooling.
The only thing that will make most home lathes get HOT is FRICTION. FRICTION will destroy your gears, ways and bearings.
As for the oils recommended, I'm sure the companies manufacturing those machines know exactly what is required to run them at the levels they were intended for. Lubrication is a must. A lot of large refiners will make certain lubricants and sell them to different distributors, who put their own label and type onto the same product distributed by their competitors. The same thing happens with reloading powders.
Gears moving through the oil, generates heat. That's why we put transmission coolers on vehicles that are under heavy load.
In the case of a lathe, generally a hobbyist won't normally run it fast enough, for long enough, for it to make a difference, but it can be done. Lots of different machines out there, with lots of different oiling systems. Best is to know what you have, and why it needs a particular oil or fluid, but in the end, any oil is better than none.
Putting, say, 10 weight oil into a gearbox designed around 80-90Wt, you will likely not like the noise levels. Conversely, if you ran 80-90Wt in a gearbox designed for 10Wt, it is liable to load up your electric motor (which may only be of marginal quality anyways, in a low end Import) and like as not, the whole system will get warm from the added friction.
The place I used to work, had 4 or 5 different oils for different machines, and different uses on the same machine. Easier to use what is called for, as a general state of affairs. But ya gotta do what ya gotta do, it won't usually cause any major problems, as long as you are using something of a similar nature to what was called for. My Colchester's manual calls for Telus 27 in the headstock and gearbox, but says if it is not available to use an oil of the specs they supply (temperature/viscosity rating stuff, looks like gibberish, but I am positive it means a lot to a Petroleum Engineer!), my Emco uses AW32 in the headstock, and my Myford uses plain old dino squeezings, 30 Wt IIRC, in a total loss system.
Use a lube oil for lube, and a cutting oil for cutting, though. I see lots of videos of guys slobbering motor oil on their work when they are cutting or drilling, ad that is counterproductive, unless the intent was to produce lots of smoke, a sign of heat, in turn, a sign of too much friction happening.
In a pinch, animal fats work OK for cutting, though they can go bad between uses, if you are not using the stuff up. Lard Oil, was commonly called out as the cutting fluid of choice, a mixture of Lard, and olive oil to thin it enough to keep it liquid.
Bacon fat works too. Salt content though, and hunger pangs!
Whether you buy some stinky pipe cutting oil, or use a emulsified oil cutting fluid (my preference), use a cutting fluid, not a lube, for cutting. FWIW, WD40 works pretty well for cutting Aluminum. The old texts called out Kerosene for that, WD40 is mostly Stodddard Solvent, which is pretty close to the same stuff.
Cheers
Trev
