  We consider the Kronecker algebra $A=\mathcal{O}[X, Y]/(X^2, Y^2)$, where
$\mathcal{O}$ is a complete discrete valuation ring. Since $A \otimes\kappa$ is
a special biserial algebra, where $\kappa$ is the residue field of
$\mathcal{O}$, one can compute a complete list of indecomposable
$A\otimes\kappa$-modules. For each indecomposable $A\otimes\kappa$-module, we
obtain a special kind of $A$-lattices called "Heller lattices". In this paper,
we determine the non-periodic component of a variant of the stable
Auslander--Reiten quiver for the category of $A$-lattices that contains "Heller
lattices". Moreover, we give the strong restrictions on stable
Auslander--Reiten quivers for symmetric orders over a complete discrete
valuation ring.
