The effects of electron-lattice (e-1) interaction in a halogen-bridged Ni complex chain are discussed. As is already known, these complexes are most suitably described as a one-dimensional Mott insulator driven by a strong on-site Coulombic repulsion on the Ni sites. In fact, we see no lattice displacement in their ground states. In doped or photoexcited states, however, there is a possibility that the e-1 interaction manifests itself as a local deformation such as a polaron or a self-trapped exciton (STE), even if the Coulombic repulsion is extremely strong. We have therefore investigated the lattice relaxations in such cases and found that the interaction is drastically suppressed in a regime of weak and moderate strength.