Lyotropic liquid crystals exhibiting nematic phases were obtained from the mixtures potassium laurate/alkali sulfate salts (M 2 SO 4 )/1-undecanol (UndeOH)/water and sodium dodecyl sulfate (SDS)/M 2 SO 4 /1-dodecanol (DDeOH)/water, where M 2 SO 4 represents the alkali sulfate salts being Li 2 SO 4 , Na 2 SO 4 , K 2 SO 4 , Rb 2 SO 4 or Cs 2 SO 4 . 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.