PbCl₄ exist, but PbBr₄ and PbI₄ do not because of

(1) PbBr₄ , PbI₄ is unstable compounds and can't exist in nature

Reason:   Iodine, Bromine are less Electronegative  hence. they can't activate (excite) the 'S' electrons present in the valence sell

(i.e Inert pair effect) and they can't oxidize the Pb⁺² to Pb⁺⁴

(2) PbF₄ , PbCl₄ are exist in nature

Reason : Fluorine , Chlorine are more Electronegative hence They can activate (excite) the 'S' electrons present in the valence sell

and oxidize the Pb⁺² to Pb⁺⁴