We investigate the temperature- and humidity-dependent mechanical response of tetragonal lysozyme crystals using a continuum-based crystal plasticity model calibrated with existing experimental data. The effects of temperature and intracrystalline water are incorporated in the elastic constant of the protein crystal as well as the critical resolved shear stress on the slip planes in the crystal plasticity model. The critical resolved shear stresses have been deduced from Vickers microhardness test data corresponding to different temperatures and states of hydration. Compression analyses have then been carried out along different crystallographic directions of lysozyme crystals which reveal that their mechanical response is highly anisotropic and orientation dependent, being purely elastic along the [110] direction but elastoplastic along the [100] and [112] directions. An interesting observation is that an increase in temperature and the amount of intracrystalline water molecules leads to a decrease in the critical resolved shear stress of the slip systems resulting in softening of the crystal. The analysis presented in this paper may be applied to the study of other protein crystal systems as well as their optimal design for biotechnological applications.