We have prepared the skutterudite-related compounds FeCo3Sb12 and La0.75Fe3CoSb12 with different average grain sizes (about 0.8 and 3.9μm) by hot pressing. Samples were characterized by XRD, EPMA and SEM. The lattice thermal conductivity was investigated in the temperature range from room temperature to 200℃. Based on the Debye model, we analyse the change in lattice thermal conductivity due to various phonon scattering mechanisms by examining the relationship between the weighted phonon relaxation time τ(ω-ωD)2 and the reduced phonon frequency ω-ωD. The effect of grain boundary scattering to phonon is negligible within the range of grain sizes considered in this study. The large reduction in lattice thermal conductivity of FeCo3Sb12 compound contributes to the electron-phonon scattering.As for La0.75Fe3CoSb12 compound, the atoms of La filled into the large voids in the structure of the skutterudite produce more significant electron-phonon scattering as well as more substitute of Fe at Co site at the same time.Moreover, the point-defect scattering appears due to the difference between the atoms of La and the void. In addition,the scattering by the rattling of the rare-earth atoms in the void is another major contribution to the reduced lattice thermal conductivity. Introducing the coupling of the electron-phonon scattering with the point-defect scattering and the scattering by the rattling of the rare-earth atom is an effective method to reduce the lattice thermal conductivity of the skutterudite-related compounds by substitution of Fe for Co and the atoms of La filled in the large voids in the skutterudite structure.