Alcohols with conc. $\mathrm{HCl}$ and $\mathrm{ZnCl}{ }_2$ follow $\mathrm{S}_{\mathrm{N}} 1$ mechanism. The order of reactivity of three class of alcohols with lucas reagent is as following: $3^{\circ}>2^{\circ}>1^{\circ}$
This order is in accordance with the order of stability of carbocation formed in the reaction. More stable the intermediate carbocation, more reactive is the alcohol. Since tertiary carbocations are most stable among the three classes of carbocations; so they are most reactive towards Lucas reagent.
Since the stability of carbocations are different so the reactivity of the three classes of alcohols with Lucas reagent is different.