Geothermal energy is a promising renewable resource for the sustainable production of heat and electricity, enabling the reduction of fossil fuel consumption and associated with greenhouse gas emissions. This study evaluates the energy performance and economic viability of an innovative, high-efficiency, geothermal-driven integrated system designed to simultaneously generate heat, electricity, desalinated water, and extract high-value chemicals—including lithium carbonate, burnt magnesia, calcium carbonate, and table salt—from geothermal brine. A novel steam-release technology is proposed for high-temperature geothermal brine (195 °C), enhancing brine mineralization and simplifying the extraction processes of these valuable components (lithium carbonate, for example). This approach enables the sustainable production of lithium for battery applications alongside renewable power generation. A comprehensive thermodynamic analysis has been conducted to assess the performance of the proposed hybrid geothermal system. The integrated system is designed to provide electrical power, cooling, space heating, hot water, desalinated water, and high-value chemical products for industrial and residential applications.