We perform an analysis of recent experimental measurements and improve the lithium interaction potentials. For 6 Li a consistent description can be given. We discuss theoretical uncertainties for the position of the wide 6 Li Feshbach resonance, and we present an analytic scattering model for this resonance, based on the inclusion of a field-dependent virtual open-channel state. We predict new Feshbach resonances for the 6 Li-7 Li system, and their importance for different types of crossover superfluidity models is discussed.