Two Li-rich candidates, TYC 1338-1410-1 and TYC 2825-596-1, were observed with the new high-resolution echelle spectrograph, LAMOST/HRS. Based on the high-resolution and high-signal-to-noise ratio (SNR) spectra, we derived stellar parameters and abundances of 14 important elements for the two candidates. The stellar parameters and lithium abundances indicate that they are Li-rich K-type giants, and they have A(Li)$_mathrm{NLTE}$ of 1.77 and 2.91 dex, respectively. Our analysis suggests that TYC 1338-1410-1 is likely a red giant branch (RGB) star at the bump stage, while TYC 2825-596-1 is most likely a core helium-burning red clump (RC) star. The line profiles of both spectra indicate that the two Li-rich giants are slow rotators and do not show infrared (IR) excess. We conclude that engulfment is not the lithium enrichment mechanism for either star. The enriched lithium of TYC 1338-1410-1 could be created via Cameron-Fowler mechanism, while the lithium excess in TYC 2825-596-1 could be associated with either non-canonical mixing processes or He-flash.
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