The years-long and high-precision photometric data observed by Kepler satellite combining with huge amount spectra observed by LAMOST (Large Sky Area Multi-Object Fiber Spectroscopy Telescope) provide a great opportunity to study the relations between surface rotation and lithium abundance of Li-rich giants. In this study, we cross match the Kepler data with Li-rich giants catalog from LAMOST, and obtain 619 common sources. Then we measure 36 rotation periods from the full set of 295 Li-rich giants with good data quality which consists of two sub-samples. The rotation periods of 14 stars were extracted from 205 stars with evolutionary stages determined using asteroseismology, including 11 core helium-burning stars (HeBs), 2 red giant branch stars (RGBs), and 1 unclassified star. All the super lithium-rich giant stars (A(Li) > 3:3 dex) are HeB in our sample. The remaining 90 giants do not have evolutionary stages confirmed, and in this sub-sample, 22 giants have their rotation period measured. The rotation detection rate of the former sub-sample is 6.8%, which is significantly higher than the detection rate of a large giant sample in previous studies (2.08%). With surface rotation period measured, we confirm the relation between stellar rotation and lithium enrichment of giants. Meanwhile, we find that the less Li-enriched stars have a relatively dispersed rotation period, and giants with high Li enrichment concentrate on the rapidly rotating area, which are consistent with earlier studies. The present work also shows a jump at A(Li)  3:3 dex in the relation between rotation period and Li abundance that coincidently is the boundary between Li-rich giants and super Li-rich giants, which may indicate different mechanisms. The rotation periods of super Li-rich giants become shorter as the lithium enrichment increases.This correlation provides evidence for the rotationally induced extra-mixing mechanism responsible for Li enrichment of giants.