Ca\(^{2+}\) (calcium ions) do not form a precipitate that is soluble in excess NaOH, or in dilute HCl, but they do form a white precipitate with NaOH that is insoluble in excess NaOH and in NH\(_3\). 

Zn\(^{2+}\) ions form a white precipitate (Zn(OH)₂) with sodium hydroxide (NaOH) that is soluble in excess NaOH and also soluble in excess ammonia (NH₃), forming a complex ion, but insoluble in dilute HCl. 

Adding NaOH to Al\(^{3+}\) solution initially forms a white precipitate of Al(OH)₃, which is then soluble in excess NaOH, but the precipitate remains insoluble in NH₃ and dilute HCl. 

Pb\(^{2+}\) ions form a white precipitate (lead(II) hydroxide, Pb(OH)\(_2\)) with both sodium hydroxide (NaOH) and aqueous ammonia (NH\(_3\)), but the precipitate is soluble in excess NaOH, but insoluble in excess NH\(_3\). It's also insoluble in dilute HCl. 

Both Pb\(^{2+}\) and Al\(^{3+}\) form white precipitates soluble in excess NaOH and insoluble in NH\(_3\) and dilute HCl. However, lead(II) chloride, PbCl\(_2\) is slightly soluble in cold HCl and more soluble in hot HCl while AlCl\(_3\) is soluble in HCl.

Since the precipitate is described as insoluble in dilute HCl, Pb\(^{2+}\) is the more likely candidate.