We report the results of surface electronic-structure calculations for the three low-index faces of elemental Pb. To our knowledge, these are the first calculations for the Pb(110) and Pb(111) surfaces addressing their electronic structure. The underlying bulk crystal is described by a realistic second-nearest-neighbor empirical tight-binding Hamiltonian which includes s and p orbitals and takes spin-orbit coupling into account. The resulting 6s- and 6p-derived bands are entirely decoupled. Our Hamiltonian yields the bulk density of states and the occupied bulk energy bands in excellent agreement with the data from x-ray and angle-resolved ultraviolet photoelectron spectroscopy measurements. The electronic structure of the (001), (110), and (111) surfaces is calculated for semi-infinite systems employing the scattering theoretical method. Our calculations predict a number of occupied as well as empty surface states or resonances in the energy regions of both the s- and p-band projections. All three surfaces show a pronounced resonance around -8 eV and a band of bound surface states near -2 eV below ${\mathit{E}}_{\mathit{F}}$. There are no surface states in the gap between the occupied s and p bands. For exemplary cases we highlight the origin and nature as well as the spatial localization of characteristic surface features.