The low-temperature phase diagrams for the quasi-binary lanthanum halogenides LaX3/LaY3 (X,Y = F, Cl, Br, I) were calculated at an ab initio level, without any recourse to experimental information. The starting point of our general approach is the global exploration of the enthalpy landscapes for many different compositions in these systems. Candidates for both ordered stoichiometric modifications and crystalline solid solution phases are identiﬁed, and their free enthalpies are computed at an ab initio level. From this the low-temperature phase diagrams are derived. We found that in all six systems under investigation only crystalline ordered phases should be present. We predict the existence of several thermodynamically stable and metastable phases in these systems.