A new Laplace transform based multistate local CC2 response method for calculating excitation energies of extended molecular systems is presented. By virtue of the Laplace transform trick, the eigenvalue problem involving the local CC2 Jacobian is partitioned along the doubles-doubles block (which is diagonal in the parental canonical method) without losing the sparsity in the integral, amplitude, and amplitude response supermatrices. Hence, only an effective eigenvalue problem involving singles vectors has to be solved, while the doubles part can be computed on-the-fly. Within this framework, a multistate treatment of excited states with state specific and adaptive local approximations imposed on the doubles part is straightforwardly possible. Furthermore, in the context of the density fitting approximation of the two-electron integrals, a procedure to specify the local approximation, i.e., the restricted pair lists and domains, on the basis of an analysis of the object to be approximated itself is proposed. Performance and accuracy of the new Laplace transformed density fitted local CC2 (LT-DF-LCC2) response method are tested for set of different test molecules and states. It turns out that LT-DF-LCC2 response is much more robust than the earlier local CC2 response method proposed before, which failed to find some excited states in difficult cases.