Potential advantages of active electrode nanomaterials have led to development of high energy and power density lithium-ion (Li-ion) batteries. However, under increasing demand for critical resources such as lithium and cobalt, it is necessary to use abundant raw materials, which can be obtained from industrial waste. In this work, purified Mg(OH)₂ from waste generated in the production of Li₂CO₃ with natural brines from the Salar de Atacama (Chile) is used as a doping agent for synthesis of LiMn₂O₄ (LMO) spinel octahedral nanoparticles co-doped with excess Li and Mg. Crystallization of a pure cubic spinel phase ( $Fd\overline{3}m$) takes place at 500 °C and sintering temperature effect at 580 and 750 °C, thus the elemental composition and the structural, morphological, and electrochemical properties are studied in detail. Optimum electrochemical performance at room temperature is obtained for Li_1.03Mg_0.05Mn_1.92O₄ spinel sintered at 750 °C with an initial discharge capacity of 121.3 mAh·g⁻¹ and capacity retention of 94.0% after 100 cycles at C/3. A locally ordered spinel structure is obtained at 750 °C, and doping with Mg²⁺ improves structural rigidity. Synergy between both effects resulted in a high Li⁺ diffusion rate (1.29 x 10⁻⁹ cm²·s⁻¹) significantly improving cycling performance at elevated C-rates in 50 °C.