Abstract The puzzle of the Li-rich giant is still unsolved, contradicting the prediction of the standard stellar models. Although the exact evolutionary stages play a key role in the knowledge of Li-rich giants, a limited number of Li-rich giants have been observed with high-quality asteroseismic parameters to clearly distinguish the stellar evolutionary stages. Based on the LAMOST Data Release 7 (DR7), we applied a data-driven neural network method to derive the parameters for giant stars, which contain the largest number of Li-rich giants. The red giant stars are classified into three stages of Red Giant Branch (RGB), Primary Red Clump (PRC), and Secondary Red Clump (SRC) relying on the estimated asteroseismic parameters. In the statistical analysis of the properties (i.e., stellar mass, carbon, nitrogen, Li-rich distribution, and frequency) of Li-rich giants, we found that (1) most of the Li-rich RGB stars are suggested to be the descendants of Li-rich pre-RGB stars and/or the result of engulfment of planet or substellar companions; (2) the massive Li-rich SRC stars could be the natural consequence of Li depletion from the high-mass Li-rich RGB stars; and (3) internal mixing processes near the helium flash can account for the phenomenon of Li richness on PRC that dominated the Li-rich giants. Based on the comparison of [C/N] distributions between Li-rich and normal PRC stars, the Li-enriched processes probably depend on the stellar mass.