The optimal response in the Lamb-Oseen vortex is studied by considering the harmonically forced problem with frequency ω. High variance levels are sustained in these systems under periodic forcing. In the axisymmetric case n=0, the response is the largest when the input frequency is zero. When considering helical perturbations n=1, large response is excited through resonance mechanism at moderate and large wavelengths. At smaller wavelengths, large response is excited by steady forcing. For perturbations with higher azimuthal wavenumbers |n|>1, the magnitudes of the response are smaller than those for helical modes. For given axial wavenumber and input frequency, the response increases rapidly with Re, which points to the significance of energy growth in high-Reynolds-number practical flows.