Thermoelectric materials convert thermal energy into electrical energy and can be a solution for the global climate crisis. For advanced thermoelectric applications, the conversion efficiency has to be high, motivating the search for materials with a high average thermoelectric figure of merit. To achieve such large thermoelectric figures of merit, the electronic properties must be maximized, and the thermal transport must be minimized over a wide temperature range. The chalcopyrite CuGaTe2 exhibits promising electronic properties but suffers from poor thermoelectric performance due to its high lattice thermal conductivity. In the present study, we perform compressive sensing lattice dynamics (CSLD) and ShengBTE calculations, which suggest that the high room temperature lattice thermal conductivity is a result of high longitudinal group velocities. To effectively reduce the thermal conductivity, we introduce lithium into three variants of CuGaTe2: pristine, Sb-doped, and Ag-doped. All compositions exhibited a significant reduction in the lattice thermal conductivity with the inclusion of lithium without any compromise to the electronic properties. By comparing the elastic moduli, we demonstrate that the reduction in the lattice thermal conductivity is to some extent the result of phonon softening. The low thermal conductivity and high power factor in Cu0.90Li0.05Ag0.05GaTe2 lead to a 56% increase in the average zT compared to the pristine sample. Due to the low cost of lithium, this approach can be adapted to chalcopyrite compounds and other thermoelectric systems to develop sustainable and affordable applications for waste heat recovery.