Limewash paint adheres best to porous surfaces. Given that you've already applied a mist coat and a coat of Dulux emulsion paint, it might hinder the absorption of the limewash into the plaster.
For the best results when using limewash over previously painted surfaces:
Clean the Surface: Ensure the wall is free from any dirt, dust, or grease.
Use a Mineral-based Primer: Before applying limewash on previously painted walls, it's a good idea to use a mineral-based primer. This will help to provide a porous surface for the limewash to bond to. Romabio's BioGrip Micro or similar products are specially formulated for such purposes.
Test Patch: Always do a test patch to see how the limewash adheres and looks over the primer and existing paint.
Multiple Coats: Remember that limewash may require multiple thin coats to achieve the desired look. Allow each coat to dry (typically 12-24 hours) before applying the next.
Protection: Once you have achieved the desired effect with your limewash, consider sealing it with a lime-compatible sealer if you desire added protection, especially in high-traffic or high-moisture areas.
Remember, while online research is useful, consulting with a local professional or paint store can provide insights specific to your region's climate and your home's unique needs.
Good luck with your project!