The quantum statistical weight (G) of an atomic energy level is an important spectroscopic parameter, its effect on the atomic ionization process is, however, usually neglected for simplicity. In this work, the influences of the G parameters of the lithium atomic energy levels are taken into account explicitly for the first time in the study on the process of three-step photo-excitation (PE) + electric field ionization (EFI), which yields a significant effect on overall EFI efficiency of the PE+EFI process. With a set of specially designed PE+EFI schemes, the expected results are obtained. First, with a three-step PE scheme, the Li atom is excited by three pulsed lasers with different wavelengths, which are fired simultaneously, to one of the Rydberg states from its ground state, from which the Li atom is ionized by an electric-field pulse with a time delay in order to avoid the Stark effect. Based on the three physical processes the atom experiences the PE, none field, and the EFI processes, and a set of universal rate equations are established according to the conservation law of particle number with the knowledge of physical mechanism of the three different processes and the physical model set up for them, respectively. The G parameters of the four relevant bound energy states are displayed explicitly in the rate equations for the PE process to offer a clear viewabout their effect on the overall EFI efficiency of the PE+EFI process. Secondly, the overall efficiencies of PE+EFI process are calculated with the Matlab programming for the two specified excitation schemes, 2S1/22P1/23S1/225P1/2, 3/2 and 2S1/22P3/23D5/225F5/2, 7/2. The overall EFI efficiency of PE+EFI process is investigated not only by adjusting the laser parameters but also by comparing the results between the two different excitation schemes. In order to establish the relationship between the overall EFI efficiency and external field quantitatively, the dependence of population rate of the relevant bound states on various factors, such as laser and atomic parameters, is calculated systematically. The role of the G parameters of the relevant atomic energy levels played in the population rates is observed to determine which excitation scheme is better in terms of the population rate of the Rydberg state. Meanwhile, the spontaneous emission of the Rydberg state during the time delay between the pulses of electric field and laser is also evaluated to make a balance between avoiding the Stark effect and minimizing the spontaneous emission. Based on the analysis of the calculations, some new results are achieved. An enhancement of the overall EFI efficiency can be obtained by making a sophisticated design on the excitation scheme of the PE+EFI process to optimize the G parameters. The time delay between the pulses of electric field and laser not only lets the atom experience a field-free time period, but also makes an upper limit for the population rate of Rydberg state due to the redistribution of atom among the four relevant bound states in the period. The upper limit is found to be dependent on neither laser parameters nor the absolute values of the G parameters, while only on the branching ratio of the G parameters among those bound states. The overall EFI efficiency is dominated by the population rate of Rydberg state, as the EFI process may ionize all Rydberg atoms once the strength of the EFI field reaches the EFI threshold of the Rydberg state. Hence, the key factor for raising the overall EFI efficiency is to enhance the population rate of Rydberg state in the PE process, which is a hard challenge due to the upper limit for the population rate of Rydberg state.