  We perform the all-loop renormalization of the O($N$) $\lambda\phi^{4}$
scalar field theory with Lorentz violation which is exact in the
Lorentz-violating $K_{\mu\nu}$ coefficients. This task is fulfilled
analytically firstly explicitly at next-to-leading order and later at all loop
levels through an induction process based on a general theorem emerging from
the exact approach. We show that the exact results reduce to the approximated
ones, previously obtained, in the appropriated limit and comment on their
implications. The current exact calculation involving such a symmetry breaking
mechanism in the referred theory is the first one in literature for our
knowledge. At the end, we analyze the effect of Lorentz violation on the
asymptotic single-particle states.
