Lithium intercalation and concomitant exchange of sodium by lithium in the second stage NaC6O0.5 graphite intercalation compound (GIC) result in the formation of new types of lithium-rich GICs. Each of them contains multilayered stackings composed of five intercalated layers, three of lithium alternating with two of oxygen. The corresponding interplanar distance d(I) is equal to 665 pm. The highest lithium concentration was found in the yellow Li2C6O0.5 compound which is a bi-intercalation compound since two successive Van der Waals (VdW) spaces are filled alternately with layers of different compositions, one containing lithium only and the other one containing the five oxygen and lithium layers. Other derived compounds have been isolated: a classical stage 3 compound composed of two empty VdW spaces and one containing the characteristic five layers stacking corresponding to an identity period along c-axis, I-c, equal to 1335 pm; a bi-intercalation compound which results in the intercalation of lithium in the two VdW spaces of the previous stage 3 compound and exhibitis a I-c value of 1405 pm. All of these lithium-rich compounds contain sodium clusters trapped in their bulk.