Metal fluorides, promising lithium-ion battery cathode materials, have been classified as conversion materials due to the reconstructive phase transitions widely presumed to occur upon lithiation. We challenge this view by studying FeF₃ using X-ray total scattering and electron diffraction techniques that measure structure over multiple length scales coupled with density functional theory calculations, and by revisiting prior experimental studies of FeF₂ and CuF₂. Metal fluoride lithiation is instead dominated by diffusion-controlled displacement mechanisms, and a clear topological relationship between the metal fluoride F⁻ sublattices and that of LiF is established. Initial lithiation of FeF₃ forms FeF₂ on the particle’s surface, along with a cation-ordered and stacking-disordered phase, A-Li_xFe_yF₃, which is structurally related to α-/β-LiMn²⁺Fe³⁺F₆ and which topotactically transforms to B- and then C-Li_xFe_yF₃, before forming LiF and Fe. Lithiation of FeF₂ and CuF₂ results in a buffer phase between FeF₂/CuF₂ and LiF. The resulting principles will aid future developments of a wider range of isomorphic metal fluorides.