Copper, silver, and gold are often found in combination. That makes sense to me, because they are members of the same chemical family. Likewise, I would expect nickel palladium, and platinum to be found together.
But lead and zinc are often found together, even though they are not of the same chemical family. At least, these metals seem to appear "jointly" more often than lead and tin, even though these are members of the same family.
Why would that be, or am I missing something?
Lead and zinc have in common two electrons in their outer "s" subshell. That is why they may sometimes have a similar behavior. You would object that lead has also two "p" electrons 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 effect 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 $7$ for $\ce{4f, 5d, 6p}$. It is $6$ for $\ce{6s}$. So the subshells $\mathrm{4f, 5d, 6p}$ are so contracted that they are mixed with inner shells and "disappear" from the periphery. Only the two electrons $\ce{6s}$ , with n+l = 6, 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 $\ce{PbSO4}$ is insoluble in water, like $\ce{BaSO4}$. 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 $2$ "s" electrons in its outer shell. By comparison, zinc is $\ce{[Ar] 3d^{10} 4s^2}$. Like $\ce{Pb}$, it also looks like a noble gas (argon) plus $2$ s electrons in its outer shell, if the filled subshell $\ce{3d^{10}}$ is "forgotten". Mother Earth is probably not able to recognize the existence of this $\ce{3d}$ shell and has often mixed $\ce{Zn}$ and $\ce{Pb}$ minerals.
We have a combination of two effects acting together:
The tendency of both metals to be found as sulfides instead of oxides
Relativistic effects impacting the valence of lead to match that of zinc.
Together these phenomena lead lead and zinc to form compounds with similar nonmetals and similar stoichiometry.
The Goldschmidt Classification
The Goldschmidt classification is a geochemical classification that identifies, as a first approximation, the predominant geochemical behavior of naturally occurring, isotopically stable elements. Among metals three of the four classes are seen, and may be described as below:
Lithophile: tend to form the oxide minerals that commonly dominate rocks.
Chalcophile: tend to form minerals with less electronegative nonmetals than oxygen, principally sulfur, found in ores of these metals.
Siderophile: tends to remain uncombined or incorporated into iron-dominated metal phases, relatively rare in the crust because they are instead largely in the iron-alloy core.
Atmophile: found in volatile or gaseous compounds, not applicable to metals.
In general, metals as they appear in the Periodic Table end up being largely segregated according to the groups where they appear. The early groups, from G1 to about G5 and also including G3-like lanthanides and actinides, most strongly prefer oxygen to less electronegative elements, are lithophilic. The middle groups, roughly to G10 or G11, are most compatible with iron and tend towards siderophile. The later groups of metals, principally from G12 on, are the chalcophiles, which have less preference for both oxygen and the iron phase and thus combine with sulfur and similar nonmetals as chalcophiles.
Zinc (G12) and lead (G14), then, are both chalcophiles and thus tend to occur in sulfides and other compounds with low-electronegativity nonmetals.
But, you say, based on electronic shell structures zinc should have a common oxidation state of +2 while lead, in a different group, should be able to reach +4. Well, there is a twist: exit Goldschmidt, enter Einstein.
Not all valence electrons are equal
As described by Maurice, in heavy atoms the $s$ electrons draw so much energy from the electrostatic field that it becomes comparable to the mass(-energy) the electron would have in Newtonian mechanics, so we see relativistic effects. Strictly speaking, only the $1s$ electrons are close enough to the nucleus to be directly affected, and the result is that the $1s$ orbital is shrunken and even more tightly bound than the nonrelativistic model would predict. But the other $s$ orbital wavefunctions remain orthogonal to the $1s$ function and to each other, so they "chase" the shrunken $1s$ orbital and themselves become shrunken and tightly bound.
With mercury this effect makes that element highly unreactive because there are no more valence electrons free from this propagated relativistic effect. But lead, two groups later, replaces the "lost" $6s$ electrons with two $6p$ electrons that avoid the "inert pair" effect. It is thus the equality between two $4s$ electrons in zinc and two (still-active) $6p$ electrons in lead that make the preferentially formed sulfides etc stoichiometrically equivalent.
