The work is performed to study the structural stability and optoelectronic properties as well as thermoelectric properties of LiCuM (M=S, Se and Te) half-Heusler semiconductors using density functional theory (DFT) and semi-classical Boltzmann transport. The ground state results show that the compounds exhibit semiconducting behavior with a direct band-gap. The elastic parameters indicate that the present compounds are mechanically, dynamically stable and brittle. The calculated optical properties in GGA and GGA+U approaches show that the dominant response in the low ultraviolet and visible energy regions. The thermoelectric properties are evaluated using the Slack model and temperature dependent relaxation time in the temperature range of 100 K to 1000 K. The response of thermoelectric properties to temperature is evaluated and discussed in detail. The figure of merit with relaxation time is found to increase with temperature and reaches the optimal values in GGA and GGA+U at 1000 K are 0.69(0.01), 0.66(0.665) and 0.67(0.778) for LiCuS, LiCuSe and LiCuTe, respectively. The lattice thermal conductivity decreases with increasing temperature. These properties make these compounds promising candidates for optoelectronic and thermoelectric devices.