[en] The striking suppression of superconductivity of La_2-xBa_xCuO₄ in a narrow range of x around 0.125 is known to be a consequence of a structural transition to a low-temperature tetragonal phase below about 60 K. Study of low-temperature lattice instabilities by x-ray diffraction revealed that in La_2-y-xTh_yBa_xCuO₄ the development of the low-temperature tetragonal phase, as well as the sharp suppression of superconductivity, is centered at x-y congruent 0.125, instead of x congruent 0.125. Therefore, the anomalous low-temperature behavior is essentially characterized by the density of carriers rather than local ionic forces, which couples with the lattice instabilities