We investigate the infrared (IR) effects of Lorentz violating terms in the gravitational sector using functional renormalization group methods similar to Reuter and collaborators (Reuter 1998 Phys. Rev. D 57 971). The model we consider consists of pure quantum gravity coupled to a preferred foliation, described effectively via a scalar field with non-standard dynamics. We find that vanishing Lorentz violation is a UV attractive fixed point of this model in the local potential approximation. Since larger truncations may lead to differing results, we study as a first example effects of additional matter fields on the RG running of the Lorentz violating term and provide a general argument why they are small.