Lithium is a fragile but crucial chemical element in the Universe, and exhibits interesting and complex behaviors. Thanks to the mass of spectroscopic data from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) medium-resolution survey (MRS), we can investigate the lithium abundances in a large and diverse sample of stars, which could bring vital help in studying the origin and evolution of lithium. In this work, we use the LiI6707.8{AA} line to derive the lithium abundance through a template-matching method. A catalog of precise lithium abundance is presented for 795384 spectra corresponding to 455752 stars from the LAMOST MRS Data Release 9. Comparing our results with those of external high-resolution references, we find good consistency with a typical deviation of {sigma}A(Li)~0.2dex. We also analyze the internal errors using stars that have multiple LAMOST MRS observations, which will reach as low as 0.1 dex when the signal-to-noise ratio of the spectra is >20. Besides, our result indicates that a small fraction of giant stars still exhibit a surprisingly high lithium content, and 967 stars are identified as Li-rich giants with A(Li)>1.5dex, accounting for ~2.6% of our samples. If one takes into account the fact that nearly all stars deplete lithium during the main sequence, then the fraction of Li-rich stars may far exceed 2.6%. This new catalog covers a wide range of stellar evolutionary stages from pre-main sequence to giants, and will provide help to the further study of the chemical evolution of lithium.