  A classical result in Morse theory is the determination of the homotopy type
of the loop space of a manifold. In this paper, we study this result through
the lens of discrete Morse theory. This requires a suitable simplicial model
for the loop space. Here, we use Milnor's $\textrm{F}^+\textrm{K}$ construction
to model the loop space of the sphere $S^2$, describe a discrete gradient on
it, and identify a collection of critical cells. We also compute the action of
the boundary operator in the Morse complex on these critical cells, showing
that they are potential homology generators. A careful analysis allows us to
recover the calculation of the first homology of $\Omega S^2$.
