A lattice system of adsorbed molecules is treated that is characterized by two bands of vibrational excitations. The first one originates from the collectivization of local high-frequency vibrations of individual molecules, which results from lateral intermolecular interactions. The second one arises due to the analogous collectivization of low-frequency resonance molecular modes, with their lifetimes governed by the coupling with substrate phonons. The temperature dependence of the spectral line shape for local vibrations is analyzed in the model that includes all kinds of cubic and quartic anharmonic coupling between high-frequency and low-frequency molecular modes in the fourth-order perturbation theory for the two-time retarded Green's functions in the coordinate-momentum representation. As shown, various processes that involve four vibrational excitations and contribute to the line broadening for local vibrations are dominated by quartic anharmonic coefficients renormalized in terms of the cubic one; the renormalization is caused by the effective anharmonic force acting on each harmonic oscillator. Based on the translation symmetry of the system in surface-parallel directions, the quasimode approximation is substantiated, which enables the spectral line shift and width for local vibrations to be expressed in terms of dispersion laws and lifetimes for low-frequency molecular modes. The results obtained permit spectral line characteristics of local vibrations to be estimated for H/Si(111) and H(D)/C(111) in nice accordance with the experimentally measured values. Lateral interactions of low-frequency modes are shown to result in their shorter lifetimes and hence in the additionally narrowed spectral lines. The contribution from lateral interactions of local vibrations proves to be significant for systems with the sufficiently wide local vibration band and low frequencies of resonance modes, as, for instance, in OH/SiO2 and 2 x 1 phase of CO/NaCl(100).