The primer question depends on what the wall is now. Fresh plasterboard generally goes through two stages, a drywall primer and then a mineral or bonding one, whereas a sound painted wall may need just the bonding stage. Either way, lime needs a porous mineral grip that bare paper and latex or acrylic paint do not provide. A primer tinted toward the finish color keeps thin areas from flashing white.
Before any primer, decide whether the existing paint is worth keeping. Walls are cleaned and patched, glossy enamel may need sanding, and peeling or chalking paint has to be removed or stabilized, since limewash is only as sound as the layer below. Some limewash lines are masonry-only and never go on drywall.