  The presence of a large amount of Li in giants is still a mystery. Most of
the super Li-rich giants reported in recent studies are in the solar
metallicity regime. Here, we study the five metal-poor super Li-rich giants
(SLRs) from GALAH Data Release 3 with their [Fe/H] ranging from -1.35 to -2.38
with lithium abundance of A(Li) $\geq$ 3.4~dex. The asteroseismic analysis
reveals that none are on the red giant branch. The average period spacing
($\Delta P$ ) values indicate giants are in the core He-burning phase. All of
them are low-mass giants (M $<$ 1.5M$_{\odot}$). The location in the HR diagram
suggests one of them is in the red clump phase, and interestingly, the other
four are much brighter and coincide with the early AGB phase. The abundance
analysis reveals that C, O, Na, Ba, and Eu are normal for giants of respective
metallicities and evolutionary phases. Further, we didn't find any strong
evidence for the presence of dust in the form of infrared excess or binarity
from the available radial velocity data. We discussed a few scenarios for the
existence of SLRs at higher luminosity, including past merger events. The
findings will help to understand the production and evolution of Li among
giants, in particular, during and the post-red clump phase.
