Lime bonds by soaking into porous mineral material. Latex and acrylic paint, and the paper face of drywall, give it nothing to soak into, so the walls take the primer system the product specifies. On new board that typically means a drywall primer followed by the mineral or bonding layer; sound existing paint frequently needs the bonding layer alone. A primer tinted toward the finish color stops thin patches from flashing bright white.
The primer can only hold if what is under it holds. That means washing off grime and grease, filling and sanding repairs, and testing the existing paint’s adhesion before anything else. Glossy enamel may need sanding, and peeling or chalky paint must be removed or stabilized. Some limewash ranges are for unpainted masonry only and are not used on drywall at all.