I have a circa 1978 Lakewood box fan, that is/can be made quiet running on low, but on med and hi it makes a very loud, growling noise like that of the initial starting of an outside A/C unit. It will do this even on low at times at a much quieter level, and if I turn the knob off/on it will stop while running on low.

The med setting can also be made to be quiet, but not very often. High speed, forgetaboutit. Bearings/bushings seem fine, have been regularly oiled front and back, and will spin down for nearly have a minute on shutdown silently. Does this sound like a bad capacitor?... Not that I am any electrical wiz, but I want to fix this old school, metal bladed fan that I think could last many more years. Thanks.

If it has a capacitor , go ahead and change it . That's pretty old for a cap .

It actually could also be the bearings.
Bearing, when they start going bad, get pitted and bumpy. This makes them very noisy even if oiled or greased. If it is a humming noise it could be burned out windings in the motor.

Any chance this is an aerodynamic noise? Are the blades, particularly the tips, free from bends, dings, etc? If you mark the fan blades with numbers, and repeatedly let the fan come to its own stopping point, is the lowest fan blade always a different number (random)? If not, this would indicate a blade weight imbalance and the heaviest blade on the bottom.

I don't have any advice or help to offer, but I have an old box fan from that era (when they were still square and had sharp corners) and at 40+ years old it moves air far better than any new box fan I've tested. If the motor or bearings ever go bad in it I'll find someone to rebuild it so I can use it for another 40 years (or whatever I've got left ).