First-principles calculations of optical and mechanical properties of LiBX2 (B= Ga,In; X= S,Se,Te) are performed using plane-wave pseudopotential method. According to the order of band gaps, the order of laser induced damage thresholds is LiGaS2 > LiInS2 > LiGaSe2 > LiInSe2 > LiGaTe2 > LiInTe2. The elastic constants of these crystals can all meet the mechanical stability conditions at normal pressure, and the plasticitics and ductilities of indium compounds are better than those of gallium compounds. Theoretical values of average static electronic dielectric constant ε1(0), average ordinary refraction index n0 and birefringence index Δn of these crystals are in good agreement with the experimental data. LiGaS2, LiInS2, LiGaSe2, LiInSe2 and LiGaTe2 compounds have the large birefringences and their absorption and reflectivity spectra are transmissible through mid- and far-IR region, so the five crystals are likely to be promising materials for nonlinear optical applications in the mid- and far-IR region.