We performed an elastic neutron scattering investigation of the molecular dynamics of lysozyme solvated in glycerol, at different water contents h (grams of water/grams of lysozyme). The marked non-Gaussian behavior of the elastic intensity was studied in a wide experimental momentum transfer range, as a function of the temperature. The internal dynamics is well described in terms of the double-well jump model. At low temperature, the protein total mean square displacements exhibit an almost linear harmonic trend irrespective of the hydration level, whereas at the temperature T(d) a clear changeover toward an anharmonic regime marks a protein dynamical transition. The decrease of T(d) from approximately 238 K to approximately 195 K as a function of h is reminiscent of that found in the glass transition temperature of aqueous solutions of glycerol, thus suggesting that the protein internal dynamics as a whole is slave to the environment properties. Both T(d) and the total mean square displacements indicate that the protein flexibility strongly rises between 0.1 and 0.2h. This hydration-dependent dynamical activation, which is similar to that of hydrated lysozyme powders, is related to the specific interplay of the protein with the surrounding water and glycerol molecules.