  A model that can simultaneously explain Dark Matter relic density and the
apparent matter anti-matter imbalance of the universe has been recently
proposed. The model requires $b$-hadron branching fractions to Dark Matter at
the per mille level. The $b$-hadrons decay to a dark sector baryon,
$\psi_{\rm{DS}}$, which has a mass in the region $940$ MeV/c$^{2} \leq
m(\psi_{\rm{DS}}) \leq 4430$ MeV/c$^{2}$. In this paper, we discuss the
sensitivity of the LHCb experiment to search for this dark baryon, covering
different types of topology and giving prospects for Runs 3 and 4 of the LHC,
as well as for the proposed Phase-II Upgrade. We show that the LHCb experiment
can cover the entire mass range of the hypothetical dark baryon.
