Context. Lyman- α (Ly α ) is the brightest emission line in star-forming galaxies. However, its interpretation in terms of physical properties is hampered by the resonant nature of Ly α photons. In order to remedy this complicated situation, the Lyman Alpha Reference Sample (LARS) was defined, enabling the study of Ly α production and escape mechanisms in 14 local star-forming galaxies. Aims. With this paper, we complement our efforts and study the global dust and (molecular) gas content as well as the properties of gas associated with photon-dominated regions. We aim to characterize the interstellar medium of LARS galaxies, allowing us to relate these newly derived properties to quantities relevant for Ly α escape. Methods. We observed LARS galaxies with Herschel , SOFIA, the IRAM 30m telescope, and APEX, targeting far-infrared (FIR) continuum and emission lines of C II158 μ m, O I63 μ m, O III88 μ m, and low- J CO lines. Using Bayesian methods we derived dust model parameters and estimated the total gas masses for all LARS galaxies, taking into account a metallicity-dependent gas-to-dust ratio. Star formation rates were estimated from FIR, C II158 μ m, and O I63 μ m luminosities. Results. LARS covers a wide dynamic range in the derived properties, with FIR-based star formation rates from ∼0.5−100 M ⊙ yr −1 , gas fractions between ∼15−80%, and gas depletion times ranging from a few hundred megayears up to more than ten gigayears. The distribution of LARS galaxies in the Σ gas versus Σ SFR (Kennicutt–Schmidt plane) is thus quite heterogeneous. However, we find that LARS galaxies with the longest gas depletion times, that is, relatively high gas surface densities (Σ gas ) and low star formation rate densities (Σ SFR ), have by far the highest Ly α escape fraction. A strong approximately linear relation is found between the Ly α escape fraction and the total gas (HI+H 2 ) depletion time. We argue that the Ly α escape in those galaxies is driven by turbulence in the star-forming gas that shifts the Ly α photons out of resonance close to the places where they originate. We further report on an extreme C II158 μ m excess in LARS 5, corresponding to ∼14 ± 3% of the FIR luminosity, which probably is the most extreme C II-to-FIR ratio observed in a galaxy (without active nucleus) to date.