Yellow metal bearing are likely to be affected by the sulphur additives in the EP oils intended for rear axles. (Such as Spiral bevel, or Hypoid. Worm axles usually having a yellow metal worm wheel will not use them, just a straight SAE 90 or 140 )
Modern Front Wheel Drive vehicles will be unlikely to use them, since the gears will be helical, rather than bevel.
Modern engine oils will contain additives which are not needed for lathe use, such as detergents, anti foaming, anti oxidant, or low viscosity index, and can withstand high temperatures. I would imagine that they are unlikely to do much damage to a lathe or a mill. You would be paying for a lot of features that you do not need and will not use.
Having said that, I have been using up my stock of engine oil on my machines over the last sixteen or more years with no apparent ill effects!
A comparatively straight oil should suffice.
.Howard