Paint Over Laquer/Shellac?

You can paint over pretty much anything. The problem is proper preperation. If you don't prep the pieces well you are more likely to have problems down the road.

I'd wipe it down with mineral spirits to clean the surface and remove any wax that might be there, sand completely with a 150 grit sandpaper, wipe down with a tack cloth, primer with an oil based primer and then paint over that with an oil or latex based paint.

If you are looking at doing those ceiling beams in the pic it'd be a LOT of work.

Yes I was looking to do the ceiling beams but sanding them down completely (or even a little) is certainly out of the question. I guess the architect's comment was on the money.

take a big amount of methyl alcohol (actually any alcohol would work, rub it on the beams and see if the color doesnt bleed onto the alky rag. If it does, its most likely shellac. In any case , fishhin is right, theres no reason why you couldnt scrape the beams to roughen their surface. Then put on a specific primer. they make primers for shellac and lacquers. If its a lacquer , then any ketone (acetone etc) will chemically scour it.
You prime it then paint with some nice color of your choice. Unless youre a paint strippin fool, then you cxan use a hand planer to remove some of the patina.
We had a heavy dark set of blackened beams in our kitchen/dining area(it was an old tavern) We had them chemically treated with a primer and then painted a lighter color. It did wonders for lightening up the area. The texture of the beams shows through
and it looks fine after 15 years. You can do it,

When I bought the house I live in seven years ago, one of the living room walls was painted black barnboard - lovely solid high sheen 20+ year old oil-based black paint which had merged/melded with the barnboard. It was prep prep prep, exactly as fishin has described. The walls are now green and white pin-stripe paint, and the room looks like it is two feet wider (which it needs). Definitely worth the trouble.