By using a semiclassical method, we present theoretical computations of the ionization rate of Rydberg lithium atoms in parallel electric and magnetic fields with different scaled energies above the classical saddle point.The yielded irregular pulse trains of the escape electrons are recorded as a function of emission time, which allows for relating themselves to the terms of the recurrence periods of the photoabsorption.This fact tus to illustrate the dynamic mechanism how the electron pulses are stochastically generated.Comparing our computations with previous investigation results, we can deduce that the complicated chaos under consideration here consists of two kinds of self-similar fractal structures which correspond to the contributions of the applied magnetic field and the core scattering events.Furthermore, the effect of the magnetic field plays a major role in the profile of the autoionization rate curves, while the contribution of the core scattering is critical for specifying the positions of the pulse peaks.