The Lithium Abundances from the Large Sky Area Multi-object Fiber
  Spectroscopic Telescope Medium-resolution Survey. I. The Method
  Standard stellar evolution model predicts a severe depletion of lithium (Li)
abundance during the first dredge-up process (FDU). Yet a small fraction of
giant stars are still found to preserve a considerable amount of Li in their
atmospheres after FDU. Those giants are usually identified as Li-rich by a
widely used criterion, A(Li) $ > 1.5$\,{\it dex}. A large number of works
dedicated to search for and investigate this minority of the giant family, and
the amount of Li-rich giants has been largely expanded, especially in the era
of big data. In this paper, we present a catalog of Li-rich giants found from
the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) survey
with Li abundances derived from a template matching method developed for LAMOST
low-resolution spectra. The catalog contains $10,535$ Li-rich giants with Li
abundances from $\sim 1.5$\,{\it dex} to $\sim 4.9$\,{\it dex}. We also confirm
that the ratio of Li-rich phenomenon among giant stars is about one percent, or
for a more expression, $1.29\%$ from our statistically important sample. This
is the largest Li-rich giant sample ever reported to date, which significantly
exceeds amount of all the reported Li-rich giants combined. The catalog will
help the community to better understand the Li-rich phenomenon in giant stars.
