  In this paper I investigate the effect of a magnetic field on the Casimir
effect due to a massless and charged fermion field that violates Lorentz
invariance according to the Horava-Lifshitz theory. I focus on the case of a
fermion field that obeys MIT bag boundary conditions on a pair of parallel
plates. I carry out this investigation using the $\zeta$-function technique
that allows me to obtain Casimir energy and pressure in the presence of a
uniform magnetic field orthogonal to the plates. I investigate the cases of the
parameter associated with the violation of Lorentz invariance being even or odd
and the cases of weak and strong magnetic field, examining all possible
combinations of the above quantities. In all cases I obtain simple and very
accurate analytic expressions of the magnetic field dependent Casimir energy
and pressure.
