Paint will stick to bare drywall paper or old latex; limewash will not, because it bonds by soaking into porous mineral material. That is why walls receive the primer system the specific product names. Fresh board generally gets two stages, a drywall primer under a mineral or bonding coat; walls with intact paint frequently skip straight to the bridging layer. Tinting that primer toward the topcoat shade is worth considering, since any thin patch would otherwise show stark white.
The checks before priming are the same ones a careful repaint needs, only less forgiving. Walls are degreased and dusted, damage is patched and sanded smooth, and old paint is checked to confirm it is still firmly bonded. Glossy enamel may need sanding, and peeling or powdery paint must be removed or consolidated, because the limewash can be no sounder than the layer beneath. A few limewash lines are made solely for unpainted masonry; on drywall, a different product is needed.