Monte Carlo or Molecular Dynamics calculations of surfaces of Lennard-Jones systems often indicate, apart from a gradual disordering of the surface called surface melting, the presence of a phase transition at the surface, but cannot determine the nature of the transition. In the present paper, we provide for a link between the continuous Lennard-Jones system and a lattice model. We apply the method for the (001) surface of a Lennard-Jones fee structure pertaining to Argon. The corresponding lattice model is a Body Centered Solid on Solid model with an extended range of interaction, showing in principle rough, flat and disordered flat phases. We observe that entropy effects considerably lower the strength of the effective couplings between the atoms. The Argon (001) face is shown to exhibit a phase transition at T = 70.5 +/- 0.5 K, and we identify this transition as roughening. The roughening temperature is in good correspondence with experimental results for Argon.