The evolution of the short range order (SRO) as a function of temperature in a Lennard-Jones model liquid with Ar parameters was determined and juxtaposed with thermodynamic and kinetic properties as the liquid was cooled (heated) at selected quenching rates and transformed to (from) crystalline solid or glassy states from an undercooled liquid. The Lennard-Jones system was studied by non-equilibrium molecular dynamics simulations of large supercells (approximately 20000 atoms) rapidly quenched or heated at constant pressure. The liquid to solid transition was identified by discontinuities in the atomic volume and molar enthalpy; the glass transition temperature was identified by the divergence of viscosity. The SRO was studied within the quasi-crystalline model (QCM) framework and compared with the Steinhardt bond order parameters. Within the QCM it was found that the SRO evolves from a bcc-like order in the liquid to a fcc-like ordering both the amorphous and crystalline solids through a bct-like short range order ( c/a=1.2) in the supercooled liquid. The trend in the SRO from the QCM compares well with that obtained with Steinhardt’s bond order parameters. The hypothesis of icosahedral order in liquids and glasses is not supported by our results.