The O-H vibrational frequency in crystalline hydroxides is either upshifted or downshifted by its crystalline surroundings. In the LiOH crystal, the experimental gas-to-solid O-H frequency upshift ("blue shift") is approximately +115 cm(-1). Here plane-wave DFT calculations for the isotope-isolated LiOH crystal have been performed and we discuss the origin of the OH frequency upshift, and the nature of the OH group and the interlayer interactions. We find that (1) the vibrational frequency upshift originates from interactions within the LiOH layer; this OH upshift is slightly lessened by the interlayer interactions; (2) the interlayer O-H center dot center dot center dot H-O interaction is largely electrostatic in character (but there is no hydrogen bonding); (3) the gas-to-solid vibrational shift for OH in LiOH(s) and its subsystems qualitatively adheres to a parabola-like "frequency vs electric field strength" correlation curve, which has a maximum for a positive electric field, akin to the correlation curve earlier found in the literature for an isolated OH- ion in an electric field.