  Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice
$L$, $\theta$ the automorphism of $V_{L}$ induced from the $-1$ symmetry of
$L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of
$\theta$. We classify the irreducible weak $V_{L}^{+}$-modules and show that
any irreducible weak $V_{L}^{+}$-module is isomorphic to a weak submodule of
some irreducible weak $V_{L}$-module or to a submodule of some irreducible
$\theta$-twisted $V_{L}$-module.
