Structural, electronic, elastic and dynamic properties of Li2TlIn were studied for the ground state (i. e. P = 0 kbar) and under pressure value of 4.53 kbar, using Density Functional Theory (DFT). The electronic band and density of states (DOS) calculations reveal that Li2TlIn crystal is in a metallic structure. Focusing on the elastic properties has shown that this compound is a ductile and mechanically stable material for both ground state and under pressure of 4.53 kbar. In addition, the phonon dispersion curve and the phonon DOS were obtained by density functional perturbation theory. Li2TlIn has negative frequency values both in the phonon distribution curve and phonon DOS graphs which indicate that Li2TlIn compound is dynamically unstable in the ground state. However, our results show that, when a pressure of 4.53 kbar is applied, the Li2TlIn crystal becomes dynamically stable.