An ab initio study of the dynamical dielectric response of bulk lead is presented. The influence of the 5d semicore states on the characteristics of the bulk plasmon is analyzed by means of first-principles pseudopotential calculations. The effects of spin-orbit interactions and local-fields are also studied in detail. The inclusion of the 5d semicore states in the valence configuration completely changes the high-energy-transfer dielectric properties of bulk Pb. In particular, it lowers the computed bulk plasmon energy by about 3.5 eV, bringing its frequency to good agreement with experimental data. In general, the high-energy-transfer dielectric response of bulk Pb is found to be shaped mostly by the interplay between the interband transitions involving the semicore 5d states and the spin-orbit coupling interaction. Local-field effects are found to affect the relative spectral weight of the high-energy excitations, while leaving their dispersion mostly unaffected.