In recent years, noticeable progress has been made in the development of alternative extraction systems characterized by greater sustainability. In this context, deep eutectic solvents (DESs) have emerged as a promising alternative to the conventional solvents commonly used in metal extraction. This work focuses on investigating the extraction of lanthanum in an aqueous solution of sulfuric acid using a deep eutectic solvent, employing molecular dynamics simulations (MD). The structural characteristics of the solvent and its interactions with the components of the aqueous solution are explored. In this study, tetraethylammonium bromide (TEABr) is combined with ethylene glycol (EG) to form a DES, in which sodium cyanide (NaCN) is subsequently solubilized. According to the results obtained from the MD simulation, the primary interactions in the DESs are established through hydrogen bonds between the bromine and the hydrogens of the methyl group of tetraethylammonium at 3.5 & Aring;, as well as between the bromine and the hydrogens of the methylene group of ethylene glycol at 3.5 & Aring;. Similarly, the main interactions between the binary DES and sodium cyanide occur through the hydrogens of the hydroxyl group of EG and the carbon of cyanide at 1.7 & Aring;, and between the oxygen of the hydroxyl group of EG and the sodium at 2.5 & Aring;. In the acidic solution, the primary interaction is highlighted between the lanthanum ion and the oxygen of the bisulfate at 2.8 & Aring;. Additionally, it is observed that the interaction between the DES and the aqueous solution occurs between the lanthanum and the oxygen of the hydroxyl group of EG, as well as between the lanthanum and the carbon of cyanide at 4.4 & Aring;. It is important to note that, when increasing the temperature from 25 to 80 degrees C, the interaction distance between the lanthanum and the carbon of cyanide decreases to 2.4 & Aring;, suggesting a possible correlation with the increase in lanthanum extraction, as experimentally observed. Overall, this study underscores the importance of considering the fundamental structural interactions of the DES with the lanthanum acid solution, providing an essential theoretical basis for future experimental investigations.