  We formulate the simplest minimal subtraction version for massive $\lambda
\phi^4$ scalar fields with $O(N)$ symmetry for generic anisotropic Lifshitz
space-times. An appropriate partial$-p$ operation is applied in the bare
two-point vertex function diagrams, which separates the original diagram into a
sum of two different integrals which are the coefficients of the corresponding
polynomials in the mass and external momentum. Within the proposed method, the
coefficient of the mass terms can be discarded and we obtain a minimal
subtraction method almost identical to the same scheme in the massless theory
in {\it every external momentum/mass subspace}. We restrict our demonstration
of the method up to three-loop order in the two-point vertex part. We verify
the consistency of our method by a diagrammatic computation of static critical
exponents, which validates the universality hypothesis.
