Lyotropic chromonic liquid crystals (LCLCs) constitute a unique variety of water-soluble mesogens that spontaneously assemble into elongated aggregates, thereby resulting in the formation of liquid crystal phases depending on the temperature and concentration. The influence of ionic additives on the aggregation of LCLC has been extensively studied, but the molecular mechanisms governing these effects remain unclear. In this investigation, we perform atomistic molecular dynamics simulations of dilute sunset yellow (SSY) LCLC solutions doped with NaCl and MgCl2 salts. Structural and dynamical properties of SSY hydration shells are considerably modified by the partial substitution of their H bonds with sodium/magnesium-sulfonate ion pairs. Although the intermolecular distance of similar to 3.4 angstrom between SSY mesogens is preserved regardless of the ionic content, the growing number of ion pairs favors the reduction of the electrostatic repulsion between mesogens, increasing the length of SSY stacks. Moreover, magnesium cations exert the strongest electrostatic effects due to their higher hydration capabilities and acute electrostatic binding to SSY. For these reasons, experimental observations of dilute SSY solutions doped with Mg2+ exhibit higher nematic-to-isotropic transition temperatures than Na+. This work provides a fundamental understanding of the influence of ionic additives on the self-assembly of diluted LCLC solutions derived from the synergistic molecular mechanisms between mesogens, the solvent, and cations.