Context. Some Galactic molecular clouds show signs of dust evolution as compared to the diffuse interstellar medium, most of the time through indirect evidence such as color ratios, increased dust emissivity, or scattering (coreshine). These signs are not a feature of all Galactic clouds. Moreover, molecular clouds in the Large Magellanic Cloud (LMC) have been analyzed in a previous study based on Spitzer and IRIS data, at 4′ angular resolution, with the use of one single dust model, and did not show any signs of dust evolution. Aims. In this present analysis we investigate the dust properties associated with the different gas phases (including the ionized phase this time) of the LMC molecular clouds at 1′ angular resolution (four times greater than the previous analysis) and with a larger spectral coverage range thanks to Herschel data. We also ensure the robustness of our results in the framework of various dust models. Methods. We performed a decomposition of the dust emission in the infrared (from 3.6 to 500 μm) associated with the atomic, molecular, and ionized gas phases in the molecular clouds of the LMC. The resulting spectral energy distributions were fitted with four distinct dust models. We then analyzed the model parameters such as the intensity of the radiation field and the relative dust abundances, as well as the slope of the emission spectra at long wavelengths. Results. This work allows dust models to be compared with infrared data in various environments for the first time, which reveals important differences between the models at short wavelengths in terms of data fitting (mainly in the polycyclic aromatic hydrocarbon bands). In addition, this analysis points out distinct results according to the gas phases, such as dust composition directly affecting the dust temperature and the dust emissivity in the submillimeter and different dust emission in the near-infrared (NIR). Conclusions. We observe direct evidence of dust property evolution from the diffuse to the dense medium in a large sample of molecular clouds in the LMC. In addition, the differences in the dust component abundances between the gas phases could indicate different origins of grain formation. We also point out the presence of a NIR-continuum in all gas phases, with an enhancement in the ionized gas. We favor the hypothesis of an additional dust component as the carrier of this continuum.