Computational investigations, concerning structural, elastic, electronic, optical, and thermometric properties of the MgLu₂X₄ (X = S, Se) spinel compounds are performed. The calculations are carried out by employing the first-principles L(APW + lo) method designed within density functional theory (DFT). Our ground-state calculations are found to be consistent with experimental data wherever available. Similarly, calculations of the elastic constants demonstrate that both MgLu₂S₄ and MgLu₂Se₄ are brittle and anisotropic in nature. The dominant bonding between the atoms is found covalent and strongly favouring their mechanical stability. From the calculations of electronic band structure, both compounds are found direct bandgap semiconductors at Γ- Γ with bandgap energy of 3.119 eV for MgLu₂S₄ and 2.480 eV for MgLu₂Se₄. Our analysis of electronic and optical parameters suggest them suitable candidates for optoelectronic devices particularly from visible to extreme violet region applications whereas the calculated results of thermoelectric properties highlight their remarkable thermoelectric response for a workable range of temperature.