We explore the posibility of the Lorentz Invariance violation that can come out from a quamtum theory of gravity. We concetrate particulary in the combination of the know elemetary particle interactions with a Planck-Scale preferred frame, the speci.c calculation lead to the conclusion that the effects of the Preferred Frame Granularity of Space-time would result in the very large effects. Finaly we conclude that the enthusiasm for improved searches for Lorentz violation should be dampened, given the existing unsuccessful searches.