Li(2)CdGeS(4) and Li(2)CdSnS(4) are novel quaternary diamond-like semiconductors (DLSs) which have been synthesized recently. We present first-principles calculations of their electronic, optical and lattice dynamic properties with the plane-wave pseudopotential method. We have found an indirect band gap of 2.78 eV for Li(2)CdGeS(4) and a direct band gap of 2.50 eV for Li(2)CdSnS(4). The serious stretching vibrations of the Ge/Sn-S and Li-S bonds may enhance their phonon energies, and cause them to exhibit high heat capacities and Debye temperatures, which are promising for nonlinear optical applications. Compared with Cu-based DLSs, Li plays a key role in enlarging the band gaps and increasing the lattice phonon energies, which would increase the thermal conductivity accompanied by an increase of the optical damage threshold.