Why are lead and zinc commonly found together?
Lead and Zinc have in common two electrons "s" in their outer shell. That is why they may sometimes have a similar behavior. You would object that Lead has also two electrons "p" in its outer shell, which are missing in Zinc. It is true. But these p electrons are "modified" and can be "forgotten" by an unusual phenomena in chemistry, namely Einstein's relativity.

When the number of protons in the nucleus is as high as about $80$, and it is $82$ for $\ce{Pb}$,  the nucleus charge is so high that the electron has to move at a relativistic speed to stay rotating around the nucleus, according to Bohr's model. Of course Bohr's model is wrong and the electron is not rotating and has no speed. But the calculations made with it are still valid, as was shown by Pekka Pyykko, Relativity and the Periodic Table, Accounts of Chemical Research, Vol. 12, No. 8 (1979) p. 276 - 281.

At relativistic speeds, the dimensions of all moving objects decrease. And Pekka Pyykko has shown that this effect is proportional to the sum of the two quantum numbers n and l. Lead has the following electronic configuration : $\ce{[Xe] 4f^{14} 5d^{10} 6s^2 6p^2}$. The sum n+l is equal to $8$ for $\ce{4f, 5d, 6p}$. It is $7$ for $\ce{6s}$. So the electrons $\ce{4f, 5d, 6p}$ are so contracted that they are mixed with inner electrons and "disappear" from the periphery. Only the two electrons $\ce{6s}$ , with n+l = 7, remain in the outer shell of the atom. That is why Lead $\ce{Pb}$ often behaves like an atom of the $2$nd column : The most usual oxidation number of Pb is $2$ (like in $\ce{Pb^{2+}}$), and not $4$ (like the $4$th column), which exists but is not frequent. Also $\ce{PbSO_4}$ is insoluble in water, like $\ce{BaSO_4}$. So $\ce{Ba}$ is made of $\ce{[Xe] 6s^2}$, and Pb may be considered as a sort of [pseudo-$\ce{Xe] 6s^2}$...

To go back to $\ce{Zn}$ and $\ce{Pb}$ configuration, relativity explains why $\ce{Pb}$ looks like a noble gas (Xenon) plus $2$ electrons "s" in its outer shell. By comparaison, Zinc is $\ce{[Ar] 3d^{10} 4s^2}$. Like $\ce{Pb}$, it also looks like a noble gas (Argon) plus $2$ electrons "s" in its outer shell, if the filled shell $\ce{4d^{10}}$ is "forgotten". Mother Earth is probably not able to recognize the existence of this $\ce{4d}$ shell and has often mixed $\ce{Zn}$ and $\ce{Pb}$ minerals.