Why does #"PbCl"_4# exist but #"PbIO"_4# does not?
PbCl₄ exists because a Pb atom has four valence electrons.
The electron configuration of Pb is [Xe] 6s²4f¹⁴5d¹⁰6p².
The inner subshells are filled, so the valence electrons are 6s²6p².
The most common oxidation state of Pb is +2, formed by the loss of the 6p electrons.
The less stable oxidation state of Pb is +4, formed by the loss of the 6p and the 6s electrons.
So PbCl₄ can exist, but it is somewhat unstable.
In PbIO₄, the periodate ion (IO₄⁻) has a charge of -1. So Pb would have a charge of +1.
Pb would have to lose just one 6p electron.
It can achieve a more stable state by losing two 6p electrons and getting down to a filled 6s subshell.
If lead periodate exists, it will probably have the formula Pb(IO₄)₂.