We study the properties of the entanglement spectrum in gapped
non-interacting non-Hermitian systems, and its relation to the
topological properties of the system Hamiltonian. Two different families
of entanglement Hamiltonians can be defined in non-Hermitian systems,
depending on whether we consider only right (or equivalently only left)
eigenstates or a combination of both left and right eigenstates. We show
that their entanglement spectra can still be computed efficiently, as in
the Hermitian limit. We discuss how symmetries of the Hamiltonian map
into symmetries of the entanglement spectrum depending on the choice of
the many-body state. Through several examples in one and two dimensions,
we show that the biorthogonal entanglement Hamiltonian directly inherits
the topological properties of the Hamiltonian for line gapped phases,
with characteristic singular and energy zero modes. The right (left)
density matrix carries distinct information on the topological
properties of the many-body right (left) eigenstates themselves. In
purely point gapped phases, when the energy bands are not separable, the
relation between the entanglement Hamiltonian and the system Hamiltonian
breaks down.