The lattice dynamics and thermal transport in Cu 2-d Se compounds were investigated via theoretical calculations, neutron measurement, and characterization of thermal properties. The results show that binary ordered Cu 2-d Se has an extremely low lattice thermal conductivity at low temperatures. The low energy multi-Einstein optic modes are the dominant approach obtaining such an extremely low lattice thermal conductivity. It is indicated that the damped vibrations of copper ions could contribute to the low energy multi-Einstein optic modes, especially for those low energy branches at 2e4 meV.