  In this work we evaluate analytically the ultraviolet divergences of
Lorentz-violating massive O($N$) $\lambda\phi^{4}$ scalar field theories, which
are exact in the Lorentz-violating mechanism, firstly explicitly at
next-to-leading order and latter at any loop level through an induction
procedure based on a theorem following from the exact approach, for computing
the corresponding critical exponents. For attaining that goal, we employ three
different and independent field-theoretic renormalization group methods. The
results found for the critical exponents show that they are identical in the
three distinct methods and equal to their Lorentz invariant counterparts.
Furthermore, we show that the results obtained here, based on the single
concept of loop order of the referred terms of the corresponding
$\beta$-function and anomalous dimensions, reduce to the ones obtained through
the earlier non-exact approach based on a joint redefinition of the field and
coupling constant of the theory, in the appropriate limit.
