Differential cross sections and spin asymmetries for leptons colliding with light and heavy targets are calculated at collision energies E e ranging from 1 eV to 0.3 GeV. For , the partial-wave phase shift analysis for solving the relativistic Dirac equation is used within an optical model potential, and for within the nuclear potential. At , the phase shift analysis is supplemented with the distorted-wave Born approximation to account for magnetic scattering. As test cases, elastic collisions of e±with 23 Na, 112 Cd and 208 Pb atoms are reported, and good agreement with available experimental data and other theoretical cross sections is obtained. For electrons, pronounced structures in the spin asymmetry occur at low energies and small scattering angles. They disappear beyond 50 keV and reappear beyond 50 MeV, being then particularly strong for spin-zero nuclei at large scattering angles. For positrons, the high-energy diffraction structures are shifted in phase with respect to those in the electron spin asymmetry. The strong reduction of the positron spin asymmetry and the quenching of the structures at low-energy is interpreted in terms of a dominating action of the nuclear potential.