Painted and new drywall walls give limewash nothing porous to absorb into, which is why it fails when brushed straight on. The product’s named primer system fixes that: typically a drywall primer and then a mineral or bonding primer on new board, and often the bonding coat alone on sound paint. Tinting some primers toward the finish color stops thin areas flashing white.
A finish only lasts as long as the layer under it. Paint that peels or chalks gets stripped or stabilized, glossy enamel may need sanding, and dust, grease and holes are dealt with before primer. Some limewash lines are made solely for unpainted masonry and do not belong on drywall at all.