  Astrophysics today faces a number of mysteries which defiant their
resolutions in spite of drastic improvements in instrumental design, better
technique being developed, and gradual improvements in theoretical and
computation methods over last decades. Primordial Lithium Puzzle is known to
stay with us for at least two decades, and it is very likely that its final
resolution will require some fundamentally new ideas, novel frameworks and a
non-conventional paradigms. We propose that Primordial Lithium Puzzle finds its
natural resolution within the so-called Axion Quark Nugget (AQN) dark matter
model. This model was invented long ago as a natural explanation of the
observed ratio $\Omega_{\rm dark} \sim \Omega_{\rm visible}$ without any
references to BBN physics. In this new paradigm, in contrast with conventional
WIMP (Weakly Interacting Massive Particle) framework the dark matter (DM) takes
the form of the macroscopically large quark nuggets without requiring any new
fields beyond the standard model physics, except for the axion. The time
evolution of these AQNs in primordial soup at $T\sim 20$ KeV suggests a strong
suppression of the abundances of nuclei with high charges $Z\geq 3$. This
suppression mechanism represents the resolution of the primordial lithium
abundance within AQN dark matter scenario.
