Herein, we report the dispersion and stabilization of graphene oxide (GO) in the polar organic solvent glycerol (C3H8O3). The GO/glycerol (0.5 mg/mL and 1 mg/mL) dispersions are found stable for about 4 months. Strong hydrogen bonding and electrostatic repulsive interactions amid solvent and solute may be responsible for the stable dispersion. Moreover, such interactions and the non-covalent bonding may also lead to the organization of GO sheets in the self-sustained anisotropic supramolecular lyotropic structures in glycerol. Two dimensional lamellar smectic lyotropic phases with surface chirality have been observed for 0.5 mg/mL and 1 mg/mL, GO/glycerol dispersions. Partial reduction of GO into rGO has been observed and confirmed by UV–Visible measurement. Graphene-based lyotropic structures exhibit ionic conductivity of micron order (S/cm) and also possesses conduction activation energy of range 13–14 kJ/mol. GO/glycerol-based Lyotropic dispersions show non-Newtonian behaviour along with the decrease in the viscosity as the GO concentration is increased. The maximum viscosity noted for these systems is ~630 mPa.s. Viscoelastic behaviour of lyotropic dispersion has been confirmed by dynamic rheology and G'/G'' [G'(storage) and G'' (loss) modulus] crossover. Rheological studies infer that such lyotropic dispersion with high viscosity can be explored for ink-jet printing and printing of flexible membrane.