Lubricating Oil

I'm guessing for your application it won't matter either way as long as you use oil. But I'm not a lubrication oil specialist so all the usual grains of salt apply here. You will find a lot of lubrication 'experts' on the web who use intuition as their main analysis tool supplemented by ample applications of urban legends.

I would go with the detergent oil....a clean bearing is a happy bearing....

King Solomon said "And I declared that the dead,
who had already died,
are happier than the living,
who are still alive.
But better than both
is the one who has never been born,
who has not seen the evil
that is done under the sun."

Could we add to the confusion by asking if a synthetic would reduce wear?

My 2 cents worth: stick with straight 20 W oil.

Multi-weight oils were developed to maintain lubricity (and viscosity) at higher temperatures in ICE's. Your light 20 weight oil is best for the lathe spindle, simply because it lubricates, there should not be a great deal of heat generated there, and this oil is thin enough to flow over the load bearing surface of your bearings.

If you are worried about dirt, foreign particles, etc. getting into your bearings, then something is really wrong with how you are operating. Main thing, do not use compressed air for cleaning around a mill or a lathe for safety reasons, but also to prevent injection of foreign metal dust, cuttings, etc. into the bearings.

My Smithy Granite 1340I seems most happy with being lubricated with my blood, sweat and tears.

No matter what I do it's not content without taking a piece of me as a souvenir any chance it gets.

After that it's whatever oil or grease that I have near me at the time and that time being maybe once every 2 - 3 years.

I cut my teeth on machinery that was 50 years old by the time I was trained on it. The rule of thumb given to me by several GRUMPY assed old machinists was.... Put the oil that it says on the machine or manual.... if you don't have any of that weight.... grab some motor oil.... ANY LUBRICATION IS BETTER THAN NO LUBRICATION. It will keep you running until you get the "correct" oil whatever it may be?!?!

My instinct tells me to use what the manual suggests. This is an old lathe, but in excellent condition. I want to keep it in excellent condition for the remainder of my life and pass it on to my son and hopefully his son.

You will discover a great deal of oil "specialists" on the web who use instinct as their fundamental investigation apparatus supplemented by plentiful uses of urban legends.

The basic rule is to use the oil which will have at the working maximal temperature still a high enough viscosity.