A room temperature structural study has been performed through the whole compositional range of the (Ce1-xLux Lux)-, O2-x/2 system by synchrotron X-ray diffraction and mu-Raman spectroscopy. Samples were synthesized by thermal treatment in air at 1373 K of coprecipitated mixed oxalates. A CeO2-based solid solution with a fluorite-type structure (F) was found to be stable up to x = 0.4, while at higher-Lu content a (F + C) biphasic region was observed, with C being the cubic atomic arrangement typical of sesquioxides of the heaviest rare earths. A comparative approach including also results deriving from other (Ce1-xREx)O2-x/2 systems (RE Gd and Sm) allowed us to conclude that the compositional extent of the F solid solution is a complex function of RE3+ size and RE compressibility. On this basis, the dependence of ionic conductivity on the RE identity was interpreted as related both to the Ce4+/RE3+ size closeness and to RE compressibility. Ce4+/RE3+ dimensional issues were also revealed to rule the appearance of the hybrid structure observed in the two aforementioned systems, consisting of the intimate intergrowth of C microdomains within the F based host lattice. Moreover, a more extended definition of F-based solid solution, including also the hybrid structure, is formulated; the latter is meant as a modification of the former, occurring when mainly RE-vacancy aggregates are incorporated into the host lattice in spite of isolated RE ions. By mu-Raman spectroscopy it was possible to demonstrate that the mechanism of oxygen vacancy formation is common to all the systems studied, provided that the structure of the F-based solid solution, also including the hybrid structure, is retained.