A first-principles study on the thermoelectric properties of the copper-based ternary phosphide CaCuP is presented. Self-energy relaxation time approximation and unified theory for lattice transport provide an accurate description of electron-phonon and phonon-phonon scattering. Our work provides an atomistic insight into its high thermoelectric performance, highlighting that nano-structuring can increase the thermoelectric figure of merit ZT by reducing the lattice thermal conductivity.