Context. The study of dust emission at millimeter wavelengths is important to shed light on the dust properties and physical structure of pre-stellar cores, the initial conditions in the process of star and planet formation. Aims. Using two new continuum facilities, AzTEC at the Large Millimeter Telescope Alfonso Serrano and MUSTANG-2 at the Green Bank Observatory, we aim to detect changes in the optical properties of dust grains as a function of radius for the well-known pre-stellar core L1544. Methods. We determined the emission profiles at 1.1 and 3.3 mm and examine whether they can be reproduced in terms of the current best physical models for L1544. We also made use of various tools to determine the radial distributions of the density, temperature, and dust opacity in a self-consistent manner. Results. We find that our observations cannot be reproduced without invoking opacity variations. New temperature and density profiles, as well as opacity variations across the core, have been derived with the new data. The opacity changes are consistent with the expected variations between uncoagulated bare grains, toward the outer regions of the core, and grains with thick ice mantles, toward the core center. A simple analytical grain growth model predicts the presence of grains of ~3–4 μm within the central 2000 au for the new density profile.