We investigate the effects of the Lee-Huang-Yang (LHY) correction on the ground-state phases of a one-dimensional spin-orbit-coupled spin-1/2 Bose-Einstein condensate system. The LHY interaction, originating from quantum fluctuations beyond 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 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 while more profoundly modulating 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, initially connecting to phase III(β=1/4) and transitioning 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