Half-Heusler compounds LiBZ (B = Al, In, Ga and Z = Si, Ge, Sn) are comprehensively investigated using state of the art full potential linearized augmented plane wave (FP-LAPW) method. Stable geometry of the compounds obtained through energy minimization procedure. Lattice constant increased while bulk modulus decreased in replacing the ions of size increasing from top to bottom of the periodic table. Band structure calculations show LiInGe and LiInSn as direct bandgap while LiAlSi, LiInGe and LiGaSn indirect bandgap semiconductors. Density of states demonstrates mixed s, p, d states of cations and anions in the valence and conduction bands. These compounds have mixed ionic and covalent bonding. Compounds show dominant optical response in the visible and low frequency ultraviolet energy region. The transport properties of the compounds are described in terms of Seebeck coefficient, electrical and thermal conductivities. The calculated figure of merit of LiAlSi is in good agreement with the recent experimental results.