Context : 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 . Aims : The aim of this work is to accurately measure the Li abundance and investigate the possible mechanisms of Li enrichment for a newly found super Li-rich giant , TYC 3251-581-1 , located near the luminosity function bump with a low carbon isotopic ratio . Methods : 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 } C to ^ { 13 } C ratio , and constrained the evolutionary status of TYC 3251-581-1 based on the BaSTI stellar isochrones . Results : The super Li-rich giant TYC 3251-581-1 has A ( Li ) = 3.51 , the average abundance of two lithium lines at \lambda = 6708 Å and 6104 Å 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 } C / ^ { 13 } C = 9.0 ) , a slow rotational velocity v \sin i = 2.2 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 ( [ C / Fe ] \sim - 0.34 ) and enhanced nitrogen ( [ N / Fe ] \sim 0.33 ) are also consistent with the sign of mixing . Conclusions : Given the evolutionary stage of TYC 3251-581-1 with the relatively low ^ { 12 } C / ^ { 13 } C , the internal production which replenishes Li in the outer layer is the most likely origin of Li enhancement for this star .