  We study mirror symmetry for orbifold Hurwitz numbers. We show that the
Laplace transform of orbifold Hurwitz numbers satisfy a differential recursion,
which is then proved to be equivalent to the integral recursion of Eynard and
Orantin with spectral curve given by the r-Lambert curve. We argue that the
r-Lambert curve also arises in the infinite framing limit of orbifold
Gromov-Witten theory of [C3/(Z/rZ)]. Finally, we prove that the mirror model to
orbifold Hurwitz numbers admits a quantum curve.
