A detailed structural analysis of the antiferromagnetic (Gz-type) lanthanum doped bismuth ferrite - Bi0.5La0.5FeO3 (Pn鈥瞞a鈥?/i>) 鈥?using variable-temperature powder neutron diffraction is reported. The analysis highlights a structural link between changes in the relative dielectric permittivity and changes in the FeO6 octahedral tilt magnitudes, accompanied by a structural distortion of the octahedra with corresponding A-site displacement along the c-axis; this behavior is unusual due to an increasing in-phase tilt mode with increasing temperature. The anomalous orthorhombic distortion is driven by magnetostriction at the onset of antiferromagnetic ordering resulting in an Invar effect along the magnetic c-axis and anisotropic displacement of the A-site Bi3+ and La3+ along the a-axis.