  Emerton's theory of Jacquet modules for locally analytic representations
provides necessary conditions for the existence of integral structures in
locally analytic representations. These conditions are also expected to be
sufficient for the integrality of generic irreducible locally algebraic
representations. In this article, we prove the sufficiency of Emerton's
conditions for some tamely ramified locally algebraic representations of
$\mathrm{GL}_{2}(D)$ where $D$ is a $p$-adic division algebra.
