  We apply the probabilistic coupling approach to establish the spatial
regularity of semigroups associated with L\'{e}vy type operators, by assuming
that the martingale problem of L\'{e}vy type operators is well posed. In
particular, we can prove the Lipschitz continuity of the semigroups under
H\"{o}lder continuity of coefficients, even when the L\'evy kernel
corresponding to L\'{e}vy type operators is singular.
