We investigate the effects of the Lee-Huang-Yang (LHY) correction on the ground-state phases of a one-dimensional spin-1/2 Bose-Einstein condensate system with spin-orbit coupling. The LHY interaction, originating from quantum fluctuations beyond the mean-field approximation, introduces an additional nonlinear term into the Gross-Pitaevskii equation, fundamentally altering the ground-state phase diagram. Using a variational method with a trial wave function, we derive the system’s ground-state energy and obtain analytical expressions for the stripe phase, plane-wave phase, and zero-momentum phase. The phase boundaries and tricritical points are determined by solving the energy minimization conditions. Numerically, we solve the same Hamiltonian via Newton iteration and construct phase diagrams using momentum and polarization as order parameters. Our results show that the LHY correction introduces a uniform, density-dependent energy shift across all phases but more profoundly modulates the stripe phase. Notably, it gives rise to a new zero-momentum phase, denoted as phase III (β = 1/4), which emerges only at low densities and exhibits a more complex energy expression than the conventional phase III(β = 0). Increasing LHY interaction significantly expands the stripe phase and phase III (β = 1/4) regions at the expense of the plane-wave phase, causing the latter to nearly vanish. This reorganization leads to a new triple point at low densities. The triple point initially connects to phase III (β = 1/4) and transitions to phase III (β = 0) as LHY interaction strengthens. In systems where intraspecies interactions exceed interspecies interactions (g₁₁ > g₁₂), the LHY modulation extends both stripe and zero-momentum phases into regimes with smaller intraspecies interactions. In the opposite regime, where intraspecies interactions are weaker (g₁₁ < g₁₂), the LHY effect shrinks the plane-wave phase, expands the zero-momentum phases, and induces the emergence of a stripe phase, creating additional triple points. In this regime, a smaller disparity between the two intraspecies interactions favors the formation of a larger stripe-phase region. As LHY interaction increases, the system undergoes a continuous quantum phase transition from plane-wave phase to stripe phase to zero-momentum phase. Theoretically, the stripe phase emerges because the LHY correction alters the curvature of the ground-state energy landscape, disrupting the original phase distribution. Physically, this suggests that strong LHY interaction can compensate for weaker intraspecies interactions. The LHY-induced expansion of the stripe-phase region provides enhanced control for investigating exotic states such as supersolids and quantum phase transitions in spin-orbit-coupled BEC systems.