Why is the reactivity of all three classes of alcohols with concentrated $HCl$ and $ZnCl_2$ (Lucas reagent) different?

(N/A) The reaction of alcohols with Lucas reagent proceeds via the formation of a carbocation intermediate,which is the rate-determining step.
The stability of carbocations follows the order: $3^{\circ} > 2^{\circ} > 1^{\circ}$.
Tertiary $(3^{\circ})$ alcohols form the most stable carbocation,making the cleavage of the $C-OH$ bond easiest.
Consequently,the reactivity order is $3^{\circ} \text{ alcohol} > 2^{\circ} \text{ alcohol} > 1^{\circ} \text{ alcohol}$.