The e,2e reaction of atomic and diatomic lithium is studied. In the atomic case, the problem is treated as a four electron system for which the conservation of the total spin produces a variety of exchange terms whose importance in the determination of the transition matrix element of the ionization process is studied systematically in a very large domain of incidence energy (50 eV to 5 keV) by applying in the small and intermediate energy domain an asymptotically exact distorted wave procedure. In the diatomic case, a model potential is employed for the K shell electrons and the problem is treated as a vertical transition from the lowest vibrational and rotational level of the fundamental electronic state1&Sgr;gofLi2to the fundamental2&Sgr;gstate ofLi2+.The comparison with experimental and recent theoretical results shows that the use of an all electron procedure improves the agreement with the experimental results. ©2002 American Institute of Physics.