We report ab initio calculations of the stability, lattice dynamics, and electronic and thermoelectric properties of cubic La3−yX4 (X=S, Se, Te) materials in view of analyzing their potential for thermoelectric applications. The lanthanum motions are strongly coupled to the tellurium motions in the telluride, whereas the motions of both types of atoms are decoupled in the sulfides. Nevertheless, this has no impact on their thermal properties because experimentally all compounds have low thermal conductivity. We believe that this is due to umklapp scattering of the acoustical modes, notably by the low-energy optical modes at about 7-8 meV found in all three chalcogenides, as in cage compounds such as skutterudites or clathrates, even though there are no cages in the cubic Th3P4 structure. We find that the energy band gap increases from the telluride to the sulfide, in good agreement with experiments. However, due to their similar band structure, we find that all three compounds have almost identical thermoelectric properties. Our results agree qualitatively with experiments, especially in the case of the telluride for which a great amount of data exists. All our results indicate that the sulfides have a strong potential for thermoelectricity and could replace tellurides if the charge-carrier concentration is optimized. Finally, we predict also a larger maximum ZT for the p-type doped materials than for the n-type doped ones, even though compounds with p doping have still to be synthesized. Thus our results indicate the possibility to make high-temperature performing thermogenerators based only on La3X4 compounds.