Why the fuss about primer? Limewash holds by soaking into porous mineral stuff. Latex, acrylic and bare drywall paper give it nothing to soak into. So you use the primer system your product specifies. New drywall: usually a drywall primer, then a mineral or bonding primer. Sound paint: often just the bonding coat. Some primers can be tinted near your final color. That way thin spots do not flash white.
Before any primer, wash off grease and dust. Fill and sand holes. Test that the old paint is stuck tight. Shiny enamel may need a scuff-sand. If the paint peels or rubs off chalky, it must be stabilized or taken off. Your limewash is only as good as what is under it. One more thing: some limewash lines are for bare masonry only and never go on drywall.