Long-lived nuclei incorporated in a lattice are submitted to fluctuating interactions exerted on them by the lattice atoms surrounding them. Two models are considered: Gaussian Markovian processes and Gaussian broadband fluctuations. The frequency spectrum of the electromagnetic radiation emitted by nuclei is the Fourier transform of the first-order correlation function, which can be expressed solely in terms of two-time and one-time averages of nuclear operators. The one-time averages, which depend on the fluctuations, can be calculated. Using the quantum regression theorem, the two-time averages are calculated as well and hence the frequency spectrum. For both models this spectrum is Lorentzian with width equal to the sum of the natural Linewidth and a lattice-induced width.