External plaster facade overcoating paint

Does that mean a mineral exterior paint would work?

A silicate paint should also still work, but please prepare with lime glaze or silicate primer. All other paints only if you sand off the old coat.
Otherwise, you will be overwhelmed with lime paint for the facade in any specialized store.

Unfortunately, it was painted with lime on my building back then.

Unfortunately? It's a great paint that has so many advantages and can be overpainted almost unlimited times with new lime paint. You should remove "unfortunately" from your sentence.

Thank you.
Do I need to wash off the lime scale or can I just apply the primer over it?

Thank you. Do I have to wash off the lime or can I just apply the primer over it?

I would first clean the facade from dirt. You don't need to do more. Then simply repaint.