  We report novel observational evidence on the evolutionary status of
lithium-rich giant stars by combining asteroseismic and lithium abundance data.
Comparing observations and models of the asteroseismic gravity-mode period
spacing $\Delta\Pi_{1}$, we find that super-Li-rich giants (SLR, A(Li)~$>
3.2$~dex) are almost exclusively young red-clump (RC) stars. Depending on the
exact phase of evolution, which requires more data to refine, SLR stars are
either (i) less than $\sim 2$~Myr or (ii) less than $\sim40$~Myr past the main
core helium flash (CHeF). Our observations set a strong upper limit for the
time of the inferred Li-enrichment phase of $< 40$~Myr post-CHeF, lending
support to the idea that lithium is produced around the time of the CHeF. In
contrast, the more evolved RC stars ($> 40$~Myr post-CHeF) generally have low
lithium abundances (A(Li)~$<1.0$~dex). Between the young, super-Li-rich phase,
and the mostly old, Li-poor RC phase, there is an average reduction of lithium
by about 3 orders of magnitude. This Li-destruction may occur rapidly. We find
the situation to be less clear with stars having Li abundances between the two
extremes of super-Li-rich and Li-poor. This group, the `Li-rich' stars ($3.2
>$~A(Li)~$> 1.0$~dex), shows a wide range of evolutionary states.
