  In this paper I study the Casimir effect caused by a charged and massive
scalar field that breaks Lorentz invariance in a CPT-even, aether-like manner.
I investigate the case of a scalar field that satisfies Dirichlet or mixed
(Dirichlet-Neumann) boundary conditions on a pair of very large plane parallel
plates. The case of Neumann boundary conditions is straightforward and will not
be examined in detail. I use the $\zeta$-function regularization technique to
study the effect of a constant magnetic field, orthogonal to the plates, on the
Casimir energy and pressure. I investigate the cases of a timelike Lorentz
asymmetry, a spacelike Lorentz asymmetry in the direction perpendicular to the
plates, and a spacelike asymmetry in the plane of the plates and, in all those
cases, derive simple analytic expressions for the zeta function, Casimir energy
and pressure in the limits of small plate distance, strong magnetic field and
large scalar field mass. I discover that the Casimir energy and pressure, and
their magnetic corrections, all strongly depend on the direction of the unit
vector that implements the breaking of the Lorentz symmetry.
