In recent years, numerous Cu-based compounds have attracted a great deal of interest for enhanced thermoelectric energy conversion. Here, we demonstrate that CuTlX (X: S, Se), a layered semiconductor, exhibits low lattice thermal conductivity (κ l) and a high thermoelectric figure of merit (ZT), using density functional theory calculations and Boltzmann transport theory beyond relaxation time approximation. To evaluate the absolute values of thermoelectric coefficients, different scattering mechanisms such as acoustic deformation potential scattering, impurity phonon scattering, and polar optical phonon scattering are analysed. This low lattice thermal conductivity, which is complemented by a low group velocity and a low phonon lifetime, accounts for the remarkable thermoelectric efficiency in these compounds. In CuTlS, the contribution of the in-plane optical phonon mode to κ l results in a decrease in its value, which might be attributed to the occurrence of Dirac-like crossings with non-trivial topological characteristics, as corroborated by the non-zero Berry curvature value. Overall, the thermoelectric behavior of both compounds is favorable at ambient temperature. Specifically, the out-of-plane direction in CuTlSe presents elevated thermoelectric performance with a high value for the thermoelectric figure of merit, with 1.08 and 1.16 for holes and electrons, respectively, at 300 K at the optimal carrier density of 1019 cm−3 , which well aids in both the electron and phonon transport. We also undertook monolayer examinations of these compounds due to the existence of van der Waals interactions, which predicted strong thermoelectric performance for both carrier concentrations at 300 K. As a result, our study presents a theoretical prediction on transport phenomena that requires experimental verification and should motivate additional research into prospective thermoelectric materials in the same crystal family for device applications. © 2022 IOP Publishing Ltd.