Li-graphite compounds were recently obtained under pressure with a Li/C ratio as high as 1/2. At ambient temperature and pressure, the system relaxes to a composition close to Li7C24, and the IR frequencies the positions of the X-ray diffraction lines and Li-7 NMR point to a lattice composed of two-lines dimensional clusters of 7 Li atoms on a substrate of 24 C atoms, but neither the calculated structure factor nor Li-7 NMR give evidence of local axial symmetry, as found for instance in LiC6. The Madelung energy of structures obtained by modifying the positions of the Li atoms in the clusters was calculated. A significant gain in stabilization was found for a radial shift of the peripheral Li atoms placing them about 3.2 Angstrom from each other within each cluster, in a configuration reminiscent of a Penrose lattice, with 5 or 6 nearest neighbors for each Li. A rough modelization of Li-Li covalency was also included by localizing some negative charge between first-neighbor Li+ ions, with a consequent further gain in stability. The Madelung energy is comparable to that of other LiCn structures (2 less than or equal to n less than or equal to 6). In all cases, energetically favorable structures are characterized by ’smooth’ local potentials of electrostatically equivalent species.