How to repaint bathroom walls that have a vent but lack an exhaust fan
1965 - test the paint for lead.

If you have lead paint, you'll need to take appropriate precautions. 

As for painting preparation, the usual - remove all flaking and peeling paint (scrape, sand, whatever it takes) back to sound substrate - if the substrate is not sound, replace it. That would be firmly attached paint, or the surface of the plaster or drywall. Depending what state that leaves the walls in, use spackle or joint compound to fill in defects and sand for an even surface, prime, paint.

Alternatively, put "remove existing wall surface, place tile backer, and tile the bathroom" on the list of options.

Your lack of powered vent does not really make the bathroom all that unusual or make painting it a particular problem - while they are common now, they were not common then, and  the main issue is 50 year old paint, not lack of a fan. If the walls are wet and deteriorating, it's probably more than the lack of a fan making them wet. The last 3 or 4 bathrooms I've repainted did not have a powered vent, and normal preparation and painting have held up fine for many years since.