  We propose a definition of the Casimir energy for free lattice fermions. From
this definition, we study the Casimir effects for the massless or massive naive
fermion, Wilson fermion, and (M\"obius) domain-wall fermion in $1+1$
dimensional spacetime with the spatial periodic or antiperiodic boundary
condition. For the naive fermion, we find an oscillatory behavior of the
Casimir energy, which is caused by the difference between odd and even lattice
sizes. For the Wilson fermion, in the small lattice size of $N \geq 3$, the
Casimir energy agrees very well with that of the continuum theory, which
suggests that we can control the discretization artifacts for the Casimir
effect measured in lattice simulations. We also investigate the dependence on
the parameters tunable in M\"obius domain-wall fermions. Our findings will be
observed both in condensed matter systems and in lattice simulations with a
small size.
