in the supergene environment you must not have a look at the cations only but take into consideration also the anions in the meteoric waters. Pb forms sulfate (anglesite) and carbonates (cerussite) as being subjected to weathering. Zn also forms carbonate (smithsonite) and silicate such as hemimorphite, too. Moreover the solubility of Zn- and Pb ions is strongly depending on the pH in an oxidizing environment. You can judge it by yourself when Pb ions are precipitated as cerussite while Zn ions are still in solution when studying the Eh-pH diagrams for the different elements in the paper attached.