The lattice thermal conductivities of silicon clathrate frameworks II and VIII are investigated by using ab initio lattice dynamics and an iterative solution of the linearized Boltzmann transport equation (BTE) for phonons. Within the temperature range 100-350 K, the clathrate structures II and VIII were found to have lower lattice thermal conductivity values than the silicon diamond structure (d-Si) by factors of 1/2 and 1/3, respectively. The main reason for the lower lattice thermal conductivity of the clathrate structure II in comparison to d-Si was found to be the harmonic phonon spectra, while in the case of the clathrate structure VIII, the difference is mainly due to the harmonic phonon spectra and partly due to the shorter relaxation times of phonons. In the studied clathrate frameworks, the anharmonic effects have larger impact on the lattice thermal conductivity than the size of the unit cell. For the structure II, the predicted lattice thermal conductivity differs approximately by a factor of 20 from the previous experimental results obtained for a polycrystalline sample at room temperature.