In this paper, we investigate the electronic, thermodynamic, Elastic and optical properties of the compound Li2CuO2 by using the density functional theory (DFT) under the Hubbard correction term U. Such approach allows us to gain an in-depth apprehension of the band structure, density of states, as well as the specific optical properties of compound Li2CuO2. Our results revealed that the studied material Li2CuO2 displays energy band gap values of 2.008 eV for the up spin structure and 1.582 eV for the down spin structure. In particular, the indirect bandgap is situated at the Γ point of the valence band maximum (VBM) and the M point of the conduction band minimum (CBM) points of the Brillouin zone. Moreover, we carried out a more precise analysis of the optical properties of the Li2CuO2 compound, including the dielectric function, absorption coefficient, conductivity, and extinction coefficient. These parameters give essential informations for evaluating the optical behavior of the Li2CuO2 in different practical applications. In particular, we have also investigated the thermodynamic properties of the studied compound, such as the heat capacity and the Debye temperature. This contributes to a better understanding of the compound's thermal behavior. We believe that our findings are of crucial importance in evaluating the material's stability and reactivity under various thermal circumstances.