  In this paper, we consider a semiclassical version of the fractional
Klein-Gordon equation on the lattice, $h{\mathbb{Z}}^n.$ Contrary to the
Euclidean case that was considered in [2], the discrete fractional Klein-Gordon
equation is well-posed in $\ell^2(h{\mathbb{Z}}^n).$ However, we also recover
the well-posedness results in the certain Sobolev spaces in the limit of the
semiclassical parameter $h\rightarrow 0.$
