Laser-produced gadolinium plasma (Gd-LPP) emerges as a promising candidate for next-generation nanolithography light sources. In this study, a dual laser pulse scheme was implemented to achieve a narrow spectral peak. By varying the pre-main pulse delay and pre-pulse laser energy, optimal conditions of 40 ns delay and 50 mJ energy were identified to improve spectral purity. Radiation hydrodynamics simulations revealed that the improved spectral purity stems from a flatter density gradient at the ablation front and a lower average electron density in the EUV emission region. Additionally, reheating the pre-formed plasma with a short main pulse mitigated plasma squeezing, resulting in an even lower electron density and thus improved spectral purity. Our findings suggest that spectral narrowing in the dual-pulse scheme, essential for better matching with multilayer reflection bandwidths, can be optimized through precise control of pre-pulse energy, pre-main delay, and main-pulse duration.