The lucas test is not used to detect a primary alcohol. You should also do a Jones Oxidation.
You didn't say what your alcohols were, but according to "The Systematic Identification of Organic Compounds" by Shriner, Hermann, Orrill, Curtin and Fuson
"Since the Lucas test depends on the appearance of the alkyl chloride as a second liquid phase, it is normally appicable only to achohols that are soluble in the reagent. This limits the test in general to monofunctional alchohols lower than hexyl and certain polyfunctional molecules."