  In this paper we consider a semiclassical version of the wave equations with
singular H\"{o}lder time-dependent propagation speeds on the lattice
$\hbar\mathbb{Z}^{n}$. We allow the propagation speed to vanish leading to the
weakly hyperbolic nature of the equations. Curiously, very much contrary to the
Euclidean case considered by Colombini, de Giorgi and Spagnolo [2] and by other
authors, the Cauchy problem, in this case, is well-posed in
$\ell^2(\hbar\mathbb{Z}^{n})$. However, we also recover the well-posedness
results in the intersection of certain Gevrey and Sobolev spaces in the limit
of the semiclassical parameter $\hbar\to 0$.
