Specifically catalyzes production of (R)-(-)-linalool, the main component of lavender essential oil. (2E)-geranyl diphosphate + H2O = (R)-linalool + diphosphate Binds 3 Mg(2+) or Mn(2+) ions per subunit. kcat is 0.039 sec(-1) with geranyl diphosphate as substrate. Optimum pH is 7.0. Belongs to the terpene synthase family.