Despite the importance of the LiFeO2 phases as cathode materials in lithium ion batteries, little is known about their crystal structures, except that they should be based on various superlattices of the NaCl-type disordered configuration. In particular, different degrees of ordering of the Li/Fe distribution are expected to be associated to these superstructures, affecting substantially the mechanisms of Li+ ion transport in the corresponding phases. In the frame of our research project on the structural properties of lithium ion conductors, we propose to collect powder diffraction data on samples of the beta, beta', and gamma polymorphs of LiFeO2 in the 25 to 800 C thermal range, in order to determine and refine their structures, to locate lithium ions, to determine the Li/Fe disorder state and then to infer the mobility pathways of Li+ ion at variable temperature.