  In this paper we consider the class of K3 surfaces defined as hypersurfaces
in weighted projective space, and admitting a non-symplectic automorphism of
non-prime order, excluding the orders 4, 8, and 12. We show that on these
surfaces the Berglund-H\"ubsch-Krawitz mirror construction and mirror symmetry
for lattice polarized K3 surfaces constructed by Dolgachev agree; that is, both
versions of mirror symmetry define the same mirror K3 surface.
