  Violation of the Lorentz symmetry has important effects on physical
quantities including field propagators. Therefore, in addition to the leading
order, the sub-leading order of quantities may be modified. In this paper, we
calculate the next to leading (NLO) radiative corrections to the Casimir energy
in the presence of two perfectly conducting parallel plates for $\phi^4$ theory
with a Lorentz-breaking extension. We do the renormalization and investigate
these NLO corrections for three distinct directions of the Lorentz violation;
temporal direction, parallel and perpendicular to the plates.
