Lyotropic chromonic liquid crystals (LCLCs) are formed by molecules with ionic groups at the periphery that associate into stacks through noncovalent self-assembly while in water. The very existence of the nematic (N) phase in the typical LCLC, the dye Sunset Yellow (SSY) is a puzzle, as the correlation length associated with the stacking, as measured in the X-ray experiments, is too short to explain the orientational order by the Onsager model. We propose that the aggregates can be more complex than simple rods and contain "stacking faults" such as junctions with a shift of neighboring molecules, 3-fold junctions, etc. We study how ionic additives, such as salts of different valency and pH-altering agents, alter the N phase of SSY purified by recrystallization. The additives induce two general trends: (a) stabilization of the N phase, caused by the mono and divalent salts (such as NaCl), and evidenced by the increase of the N-to-I transition temperature and the correlation length; (b) suppression of the N phase manifested in the decrease of the N-to-I transition temperature and in separation of the N phase into a more densely packed N phase or the columnar (C) phase, coexisting with a less condensed I phase. The scenario (b) can be triggered by simply increasing pH (adding NaOH). The effects produced by tetravalent spermine fall mostly into the category (b), but the detail depends on whether this additive is in its salt form or a free base form. The base form causes changes through changes in pH and possible excluded volume effects whereas the salt form might disrupt the structure of SSY aggregates.