The x-ray diffraction of the nonsuperconducting ternary fulleride Li2CsC60 reveals at room temperature a face-centered-cubic (Fm3m) disordered structure that persists to a temperature of 13 Kelvin. The crystal structure is best modeled as containing quasispherical [radius of 3.556(4) angstroms] C-60(3-) ions, in sharp contrast to their orientational state in superconducting face-centered-cubic K3C60 (merohedral disorder) and primitive cubic Na2CsC60 (orientational order). The orientational disorder of the carbon atoms on the C-60(3-) Sphere was analyzed with symmetry-adapted spherical-harmonic functions. Excess atomic density is evident in the (111) directions, indicating strong bonding Li+-C interactions, not encountered before in any of the superconducting alkali fullerides. The intercalate-carbon interactions and the orientational state of the fullerenes have evidently affected the superconducting pair-binding mechanism in this material.