New lithium rich graphite intercalation compounds have been synthesized. They display a van der Waals space containing five alternating intercalated layers, three of lithium and two of oxygen corresponding to an interplanar distance d(I) equal to 665 pm. The compound ideally formulated as Li2C6O0.5 has been obtained from the second-stage NaC6O0.5 either by its electrochemical reduction in LiClO4-ethylene carbonate electrolyte or by its direct reduction with molten lithium. This yellow material, of biintercalation type, is characterized by a repeat distance along c-axis, I-c, equal to 1035 pm. This value corresponds to the addition of an interplanar spacing of 370 pm resulting in lithium intercalation in the van der Waals gap of NaC6O0.5 and of another one of 665 pm, resulting in the exchange of sodium by lithium in the five intercalated layers of the starting material. Another compound, formulated as LiC6O0.5, is a classical stage 3 material in which the intercalated part is the five alternating lithium-oxygen layers also present in Li2C6O0.5. Its repeat distance along c-axis is equal to 1340 pm. All these LixC6O0.5 compounds contain sodium clusters trapped in their bulk. Lithium species appear to be organized to form a hexal structure as in LiC6 while there is no occurrence for a structural organization of oxygen present as peroxide ions.