The reaction between Alcohols and Lucas reagent results in the formation of precipitates of Alkyl halides. The mechanism involves the formation of a Carbocation intermediate. Thus, the stability of the Carbocation intermediate dictates the rate of the reaction.
Thus, the order of reactivity of alcohols is 3°>2°>1°
Primary alcohols yield 1° carbocations which are least stable and hence they do not produce any turbidity with Lucas reagent.
Secondary alcohols produce 2° carbocations which are of moderate stability and thus forms turbidity with Lucas reagent after 5 minutes.