  Given a complex simple Lie algebra $\mathfrak g$ and a dominant weight
$\lambda$, let $\mathcal B_\lambda$ be the crystal poset associated to the
irreducible representation of $\mathfrak g$ with highest weight $\lambda$. In
the first part of the article, we introduce the \emph{crystal pop-stack sorting
operator} $\mathsf{Pop}_{\lozenge}\colon\mathcal B_\lambda\to\mathcal
B_\lambda$, a noninvertible operator whose definition extends that of the
pop-stack sorting map and the recently-introduced Coxeter pop-stack sorting
operators. Every forward orbit of $\mathsf{Pop}_{\lozenge}$ contains the
minimal element of $\mathcal B_\lambda$, which is fixed by
$\mathsf{Pop}_{\lozenge}$. We prove that the maximum size of a forward orbit of
$\mathsf{Pop}_{\lozenge}$ is the Coxeter number of the Weyl group of $\mathfrak
g$. In the second part of the article, we characterize exactly when a type $A$
crystal is a lattice.
