Given its ubiquitous presence in the environment of bio-macromolecules, water is well known to play a fundamental part in biological activity, often as a regulating agent. In parallel, with increasing attention focused on the potential damage of microwave-frequency radiation exposure to human health, the effects of extraneous electric and electromagnetic (e/m) fields on water shells surrounding proteins, and, indeed, biomolecules themselves, are becoming a particularly pertinent issue. In this study, non-equilibrium molecular dynamics simulations of hydrated hen-egg white lysozyme have been performed in both the absence and presence of external electric fields of varying intensity (0.005-0.02 V/Å) and frequency (static, i.e., zero-frequency, together with oscillating fields of 2.45-100 GHz). By comparing the effect of different electric-field conditions on both the protein's and surrounding hydration layer's dipole moments and their underlying relaxation dynamics, clear and evident non-thermal field effects were observed on the dipolar response of both the protein and hydration layer. This occurred primarily as a consequence of the protein's dipolar alignment with the external field and increased with the growth of field intensity. In addition, it was found that the lag time of dipolar response to the applied field itself, for both the protein and the first hydration sub-shell (i.e., directly adsorbed layer), under oscillating fields is longer than that in both the second hydration sub-layer and bulk water, owing to strong direct protein-water adsorption. In that respect, we also probe and discuss the effect of protein-water hydrogen bonds, dissecting the subtleties of "bio-water" dipolar response.