In this paper we study a novel means of coupling neutrinos to a Lorentz violating background k-essence field. We first look into the effect that k-essence has on the neutrino dispersion relation and derive a general formula for the neutrino velocity
in the presence on a k-essence background. The influence of k-essence coupling on neutrino oscillations is then considered. It is found that a non-diagonal k-essence coupling leads to an oscillation length that goes like lambda sim E^{-1} where E is the energy. This should be contrasted with the lambda sim E dependence seen in the standard mass-induced mechanism of neutrino oscillations. While such a scenario is not favored experimentally, it places constraints on the interactions of the neutrino with a cosmological k-essence scalar background by requiring it to be flavor diagonal. All non-trivial physical effects discussed here require the speed of sound to be different from the speed of light and hence are primarily a consequence of Lorentz violation.
