Lithium carbide (Li2C2), a promising tritium breeding material with potential applications in magnetic confinement-based fusion reactor blankets, has drawn significant attention due to its recent utilization in lithium-ion batteries. In the current study, we employed first-principles calculations with van der Waals (vdW) force correction to explore the structural and mechanical properties of Immm and Pnma phases of Li2C2 subjected to external hydrostatic pressure. It is demonstrated that inclusion of vdW effects accurately predicts Immm→Pnma phase transition at 16 GPa, aligning closely with experimental transition pressure. In contrast, PBE-GGA calculations underestimate the same by about 21%. Current paper is the first comprehensive study of pressure evolution of mechanical properties and strength determining parameters of Li2C2. Interestingly, this inherently brittle material exhibits ductile characteristics beyond 7.5 GPa. The paper also offers a quantitative comparison of its strength parameters with other prominent tritium breeding materials. Finally, the strong directional dependence due to the presence of C2 dimer is investigated by analyzing the pressure variation of elastic anisotropy. The study has its relevance in assessing structural integrity of Li2C2 during inadvertent buildup of tritium and helium that would generate stress in the solid breeder.