Scheme for the formation of lamellar smectic phases in GO/Glycerol dispersion. Display omitted •Reporting first time the dispersion of GO in glycerol which is stable up to 120 days.•Formation of lamellar smectic structures with surface chirality.•In-situ reduction of GO to rGO during sonication within 1 h.•Higher viscosity of GOLLC systems and their viscoelastic behaviour.•G′/G′′ ratio lie between 1 and 2.4 which enable the spray coating and ink jet printing applications of studied GOLLC systems. 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.