Adsorption of L-lysine (or, in absolute nomenclature, S-lysine) on Cu(001) has been studied with a UHV-STM. The binding energy is estimated to be not lower than 1.6 eV, and thus lysine is expected to be in its anionic form on the surface. The adsorbates have two phases, that is, the two-dimensional (2D) gas and solid phases. We speculate that in the 2D gas phase the molecules stand upright on the surface with their two oxygen atoms at the atop sites and can diffuse frequently, and that in the 2D solid phase the molecules lie down on the surface and connect to their neighboring molecules by hydrogen bonds so to form two slightly different superstructures, Cu(001)((4)(1)(-2)(4))- and Cu(001)((4)(1)(-3)(4))-L-lysine, for which models have been proposed for further investigation. Surprisingly, adsorption of L-lysine can make all steps restructuring into {3 1 17} facets with the same chirality. This phenomenon shows that chiral metal surfaces have potential in discrimination of molecular chirality.