In this Letter , we report on a low-resolution spectroscopic survey for Li-rich K giants among 2000 low mass ( M \leq 3 M _ { \odot } ) giants spanning the luminosity range from below to above the luminosity of the clump .
Fifteen new Li-rich giants including four super Li-rich K giants ( \log \epsilon ( Li ) \geq 3.2 ) were discovered .
A significant finding is that there is a concentration of Li-rich K giants at the luminosity of the clump or red horizontal branch .
This new finding is partly a consequence of the fact that our low-resolution survey is the first large survey to include giants well below and above the RGB bump and clump locations in the HR diagram .
Origin of the lithium enrichment may be plausibly attributed to the conversion of ^ { 3 } He via ^ { 7 } Be to ^ { 7 } Li by the Cameron-Fowler mechanism but the location for onset of the conversion is uncertain .
Two possible opportunities to effect this conversion are discussed : the bump in the first ascent of the red giant branch ( RGB ) and the He-core flash at the tip of the RGB .
The finite luminosity spread of the Li-rich giants serves to reject the idea that Li enhancement is , in general , a consequence of a giant swallowing a large planet .