  We prove the hard Lefschetz duality for locally conformally almost K\"{a}hler
manifolds. This is a generalization of that for almost K\"{a}hler manifolds
studied by Cirici and Wilson. We generalize the K\"{a}hler identities to prove
the duality. Based on the result, we introduce the hard Lefschetz condition for
locally conformally symplectic manifolds. As examples, we give solvmanifolds
which do not satisfy the hard Lefschetz condition.
