Silicon-lithium clusters are promising candidates for hydrogen storage due to their lightweight composition, high gravimetric capacities, and favorable non-covalent binding characteristics. In this study, we employ density functional theory (DFT), global optimization (AUTOMATON and Kick-MEP), and Born-Oppenheimer molecular dynamics (BOMD) simulations to evaluate the structural stability and hydrogen storage performance of key Li-Si systems. The exploration of their potential energy surface (PES) reveals that the true global minima of Li6Si6 and Li10Si10 differ markedly from those of the earlier Si-Li structures proposed as structural analogs of aromatic hydrocarbons such as benzene and naphthalene. Instead, these clusters adopt compact geometries composed of one or two Si4 (Td) units and a Si2 dimer, all stabilized by surrounding Li atoms. Motivated by the recurrence of the Si4-Td motif, we explore oligomers of Li4Si4, which can be viewed as electronically transmuted analogues of P4, confirming the additive H2 uptake across dimer, trimer, and tetramer assemblies. Within the series of Si-Li clusters evaluated, the Li12Si5 sandwich complex, featuring a sigma-aromatic Si510- ring encapsulated by two Li65+ moieties, achieves the highest hydrogen capacity, adsorbing 34 H2 molecules with a gravimetric density of 23.45 wt%. Its enhanced performance arises from the high density of accessible Li+ adsorption sites and the electronic stabilization afforded by delocalized sigma-bonding. BOMD simulations at 300 and 400 K confirm their dynamic stability and reversible storage behavior, while analysis of the interaction regions confirms that hydrogen adsorption proceeds via weak, dispersion-driven physisorption. These findings clarify the structure-property relationships in Si-Li clusters and provide a basis for designing modular, lightweight, and thermally stable hydrogen storage materials.