Lithium metal batteries (LMBs) boast extremely high energy densities, making them promising candidates for next-generation batteries and crucial for the renewable energy transition. However, their practical application necessitates optimized electrolyte formulations. This study explores the development of advanced electrolytes for LMBs by addressing critical challenges such as compatibility and liquid window issues in electrolyte composition. Utilizing the COSMO-RS method, we developed an automated solid-liquid equilibria (SLE) search computational framework to evaluate mixing free energy, bubble points, and eutectic points in multi-component systems. Key findings highlight the significance of propylene carbonate (PC) and tetramethylene sulfone (TMS) as primary components. The addition of fluoroethylene carbonate (FEC) enhances thermal stability at high temperatures, while 1,1,2,2-tetrafluoroethyl-2,2,3,3-tetrafluoropropyl ether (TTE) lowers the eutectic point to approximately 150 K or lower, making it suitable for low-temperature operation. Moreover, our SLE search approach can be extended to explore potential compositions in higher-dimensional phase diagrams (e.g., quaternary mixtures). These advancements enable stable performance across diverse operating conditions. Overall, this investigation provides a robust theoretical foundation for next-generation electrolyte design by leveraging computational insights to guide the formulation of thermodynamically stable electrolytes essential for advanced energy storage applications.