A theoretical multiscale approach combining density functional theory and four-flux calculations based on the radiative transfer theory is used to prospect the optical properties of nanocomposite materials composed of inorganic nanoparticles of lanthanum-containing compounds (${\mathrm{LaF}}_3$ or ${\mathrm{LaPO}}_4$) embedded in Poly(methyl methacrylate) (PMMA). This theoretical investigation shows that a potential route to produce lead-free x-ray shielding screens with high transparency in the visible range ($>70\%$ of incident light) may consist in incorporating colorless ${\mathrm{LaF}}_3$ or ${\mathrm{LaPO}}_4$ spherical particles with a diameter lower than 6 nm in a PMMA panel from a minimum thickness of 3 mm with a volumetric fraction of at least 10%. In terms of x-ray attenuation, this would lead to lead equivalency of 0.1 mm (lead foil).