The application of the Lorentz integral transform (LIT) method to photon scattering off nuclei is presented in general. As an example, elastic photon scattering off the deuteron in the unretarded dipole approximation is considered using the LIT method. The inversion of the integral transform is discussed in detail, paying particular attention to the high-energy contributions in the resonance term. The obtained E1 polarizabilities are compared to results from the literature. The corresponding theoretical cross section is confronted with experimental results confirming, as already known from previous studies, that the E1 contribution is the most important one at lower energies.