Based on the extended closed-orbit theory with the combination recurrence induced by the nuclear core scattering，we calculate the time-dependent auto-ionization rate of lithium atoms in parallel electric and magnetic fields, and the chaotic behavior in the auto-ionization process is explained. A qualitative description of the shape of the ionizing trajectories from the nesting distinct fractal epistrophes is given.In particular, some special escape trajectories induced by core-scattering is obtained in configuration space. The escape time and the auto-ionization rate that exhibit a series of chaotic pulse train are discussed for different magnetic fields. We find that, with the increase of the magnetic field, the ionizing electron pulse train along with the corresponding ionized electron trajectories become more and more complicated, showing the sensitive dependence of the dynamic properties on the initial conditions.