  In this paper, we first classify all irreducible modules of the vertex
algebra $V_L^+$ when $L$ is a negative definite even lattice of arbitrary rank.
In particular, we show that any irreducible $V_L^+$-module is isomorphic to a
submodule of an irreducible twisted $V_L$-module. We then extend this result to
a vertex algebra $V_L^+$ when $L$ is a nondegenerate even lattice of finite
rank.
