Lyotropic liquid crystals exhibiting nematic phases were obtained from the mixtures potassium laurate/alkali sulfate salts (M2SO4)/1-undecanol (UndeOH)/water and sodium dodecyl sulfate (SDS)/M2SO4/1-dodecanol (DDeOH)/water, where M2SO4 represents the alkali sulfate salts being Li2SO4, Na2SO4, K2SO4, Rb2SO4 or Cs2SO4. The birefringences measurements were performed via laser conoscopy. Our results indicated that cosmotropic and chaotropic behaviors of both ions and head groups are very important to obtain lyotropic biaxial nematic phase. To obtain the biaxial nematic phase, surfactant head group and ion present in lyotropic mixture have relatively opposite behavior, e.g. one more cosmotropic (more chaotropic) other less cosmotropic (less chaotropic) or vice versa.