We study ab initio computations of the interaction of lithium with a strong laser field. Numerical solutions of the time-dependent fully correlated three-particle Schrodinger equation restricted to the one-dimensional soft-core approximation are presented. Our results show a clear transition from nonsequential to sequential double ionization for increasing intensities. Nonsequential double ionization is found to be sensitive to the spin configuration of the ionized pair. This asymmetry, also found in experiments of photoionization of Li with synchrotron radiation, shows evidence of the influence of the exclusion principle on the underlying rescattering mechanism.