Some information on lubricants for Oilite bearings is provided here:
http://www.bearing.co.il/OILITE.pdf.
From page 4 of that document:
“Oilite bearings are vacuum impregnated with a filtered oxidation and corrosion inhibited turbine oil.”
Considering the long life (perhaps a decade or so) expected of these bearings and their lubricants, oxidation inhibition is a key aspect. Even at moderate temperatures, oxidation (which results in thickening and the formation of gums, etc.) still takes place, albeit slowly. (The oxidation rate approximately doubles for every 10°C rise in temperature.) Something to note is that yellow metals, as often used in the bearing types at interest, are quite pro-oxidant.
Turbines oils are very well oxidation inhibited. So are modern engine oils. But straight mineral so-called engine oils intended for vintage equipment are much less likely to contain oxidation inhibitors in any quantity, if at all, so are contra-indicated. Modern engine oils are generally reasonably benign in terms of matrails compatibility. The zinc dithiophosphate additives (or really their degradation products) that are almost universally used in engine oils are, in isolation, potentially corrosive to yellow metals, but the detergent-dispersant systems of engine oils provide an alkaline and peptizing environment that neutralizes and/or sequesters the potentially harmful molecules.
Cheers,