The melting point for lauric acid is about 45 degrees while it is 121 degrees for naphthol. So, in a mixture repeated cycles of slow warming and cooling should separate out lauric acid from naphthol. You can improve the efficiency by adding a dash of slightly acidic 70% isopropyl alcohol. This will deprotonate the lauric acid while maintaining the proton on naphthol during this process to enhance separation and purification of the two compounds. You could also flat-out distill the two products by maintaining the temperature of the solution at the boiling point of lauric acid to separate it from naphthol. This might also be a good polishing method.
45 degrees...........what? Can't believe they give bachelors degrees to people who don't even use units these days