A confirmatory test for $Pb^{2+}$ ions involves the formation of a specific compound that indicates the presence of lead ions in a solution.

Let's go through the options:

Option A: Lead chromate ($\mathrm{PbCrO}_4$) forms a yellow precipitate, which is a confirmatory test for $Pb^{2+}$ ions.

Option B: Lead iodide ($\mathrm{PbI}_2$) forms a yellow precipitate, which is a confirmatory test for $Pb^{2+}$ ions.

Option C: Lead sulfate ($\mathrm{PbSO}_4$) forms a white precipitate, which is a confirmatory test for $Pb^{2+}$ ions.

Option D: Lead nitrate ($\mathrm{Pb(NO_3)_2}$) is soluble in water and does not form a precipitate under normal conditions. Thus, its formation is not used as a confirmatory test for $Pb^{2+}$ ions.

So, the correct answer is Option D: lead nitrate.