As often as the airbrush needs it, but not so often as to get lube into your paint.
It’s not really a question of schedule like changing your car oil every 3000 miles. There’s only two places on an airbrush that require lube and an optional set of locations.
The Needle Packing O-Ring
The piece, deep inside the airbrush, needs just a little lube to let the needle pass through it without problems.
Notes: Teflon Needle Packing O-Rings don’t need lube, but the action still tends to feel better if you do.
Screw threads don’t NEED lube. In fact, I prefer beeswax since it’s natural, but lube works too. It works as a temporary, non-drying sealant to keep various kinds of leaks from happening. Not to mention it ‘feels’ better to screw things together that have a little lube between them.