The total cross sections for positron scattering by lithium at intermediate energies (10-200eV) are calculated by using the coupled-channel optical method with a complex equivalent-local polarization potential which incorporates ionization continuum and positronium (Ps) formation channels contributions into the coupled channels framework.The effects of the two-body Ps rearrangement and three-body ionization process on the total cross section are found to be significant at lower energies and this effect is not negligible up to 30eV.Compared to the available theoretical data, the predicted total cross sections agree quite well with the calculations of McAlinden et al.