  Applying the counterterm method in minimal subtraction scheme we calculate
the three-loop quantum correction to field anomalous dimension in a
Lorentz-violating O($N$) self-interacting scalar field theory. We compute the
Feynman diagrams using dimensional regularization and $\epsilon$-expansion
techniques. As this approximation corresponds to a three-loop term, to our
knowledge this is the first time in literature in which such a loop level is
attained for a LV theory.
