Lignin is an essential yet underutilized component in biomass valorization. A majority of molecular dynamics (MD) studies on lignocellulosic dissolution via DESs use choline chloride as a hydrogen bond acceptor (HBA). In contrast, this study adopts a lignin-first approach, employing tetraethylammonium chloride (TEAC) as the HBA, to better understand how alternative DES formulations modify lignin–cellulose interactions and propose avenues for selective lignin dissolution. All-atom MD simulations were performed on a representative lignin–cellulose complex solvated in two binary DES systems: TEAC:urea (1:2) and TEAC:lactic acid (1:2). Each system underwent energy minimization, equilibration, and 300 ns production runs at 373.15 K and 1 bar using the CHARMM36 force field. Analyses included RMSD, solvent-accessible surface area (SASA), hydrogen bonding, radial distribution function, and interaction energies, with emphasis on lignin responses. Results showed that cellulose remained structurally robust in both solvents. Lignin, however, displayed marked solvent-dependent differences in stability. In the TEAC:urea system, lignin maintained a comparatively stable conformation, with hydrogen bonding largely preserved and solvent interactions being less disruptive. In contrast, lignin was noticeably more unstable in TEAC:lactic acid, where solvent penetration was stronger, hydrogen bonds were disrupted more extensively, and DES–lignin interactions proved more destabilizing. These contrasting behaviors underline the importance of solvent environment in driving lignin conformational changes. By prioritizing lignin behavior and employing TEAC as an alternative HBA, this study highlights solvent-specific mechanisms for lignin dissolution, offering molecular-level guidance for lignin-first biomass processing and broadening the design space for green DES formulations beyond choline chloride.