I found some differences Pb, Zn and Ca properties (e.g., ionic radius, polyani potential, hardness index...). For example, Cu and Zn radi are much closer to each other (0.73Å, 0.74Å), but not Pb (1.19Å).
I have made an intensive research on the topic. I came to a conclusion that the matter needs to be re-checked again because, despite the explanations given, something is still to be unveiled.
Pb and Zn in carbonates typically occur as PbS & ZnS crystalline fracture filling cements &/or as fracture related matrix alteration zones in the carbonate host rock. The occurrences I have seen appear to be of relatively late hydrothermal origin whereas the carbonate host rock is a primary sedimentary deposit. Why then the association? The Pb and Zn are sourced from deeper parts of the basin fill and are carried in watery solution till those fluids come into contact with either a sulphur containing rock, or alternatively the water cools so much that these metals are no longer soluble. Most carbonates contain significant quantities of sulphur in various organic compounds ( that’s why oil and gas hosted in carbonates are commonly ‘sour’ (= relatively rich in sulphur)). As soon as the ascending Pb an Zn bearing hydrothermal fluids that preferentially move along fracture zones contact a sulphur containing limestone these two metals will form insoluble sulphides that precipitate as fracture cements.