Spin-polarized electron pairs are generated following the ionization of the valence electron of polarized Li atoms by polarized low-energy electron impact. It is shown that the shapes of energy-sharing spectra of the pairs are influenced by an interplay of structures resulting from binary-encounter and exchange effects of the two electrons. The spin asymmetry is measured at an excess energy as low as 20 eV and compared with dynamical calculations of different models. The shape of the asymmetry is explained on the grounds of symmetry and dynamics.