The lithium abundances in a few percent of giants exceed the value predicted by the standard stellar evolution models, and the mechanisms of Li enhancement are still under debate. The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) survey has obtained over six million spectra in the past five years, and thus provides a great opportunity to search these rare objects and to more clearly understand the mechanisms of Li enhancement. Based on the high-resolution spectrum we obtained the stellar parameters ($T_mathrm{eff}$, $log g$, [Fe/H]), and determined the elemental abundances of Li, C, N, $alpha$, Fe-peak, r-process, s-process elements, and the projected rotational velocity. For a better understanding of the effect of mixing processes, we also derived the $^{12}rm{C}$ to $^{13}rm{C}$ ratio, and constrained the evolutionary status of TYC,3251-581-1 based on the BaSTI stellar isochrones. The super Li-rich giant TYC,3251-581-1 has $rm{A(Li)} = 3.51$, the average abundance of two lithium lines at $lambda = 6708$ AA and 6104 AA based on the non-local thermodynamic equilibrium (NLTE) analysis. The atmospheric parameters show that our target locates on the luminosity function bump. The low carbon isotopic ratio ($^{12}rm{C}/^{13}rm{C} = 9.0 $), a slow rotational velocity $vsin i = 2.2 rm{km,s}^{-1}$, and no sign of IR excess suggest that additional mixing after first dredge up (FDU) should occur to bring internal synthesized Li to the surface. The low carbon ($[rm{C}/rm{Fe}] sim -0.34$ ) and enhanced nitrogen ($[rm{N}/rm{Fe}] sim 0.33$) are also consistent with the sign of mixing. Given the evolutionary stage of TYC,3251-581-1 with the relatively low $^{12}rm{C}/^{13}rm{C}$, the internal production which replenishes Li in the outer layer is the most likely origin of Li enhancement for this star.
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