The energy dependence of the spin asymmetry in elastic scattering of polarized electrons from Li atoms has been studied for scattering angles of 65\ifmmode^\circ\else\textdegree\fi{}, 90\ifmmode^\circ\else\textdegree\fi{}, and 107.5\ifmmode^\circ\else\textdegree\fi{} and collision energies from 1 to 30 eV. The measured asymmetry shows variations between its extreme values of + 1 and - ⅓, and its behavior can best be described by close-coupling calculations.