Why is the reactivity of all the three classes of alcohols with cone. HCl and $ZnC{{l}_{2}}$ (Lucas reagent) different?

carbocation, more reactive is the alcohol.

Tertiary carbocations are most stable among the three classes of carbocations and the order of the stability of carbocation is 3°>2°>1°. This order, in turn, reflects the order of reactivity, of three classes of alcohols, i.e. 3° >2° >1°.

Thus, as the stability of carbocations are different so the reactivity of all the three classes of alcohols with Lucas reagent is different.