  We study a Lindbladian generalization of the Anderson model of localization
that describes disordered free fermions coupled to a disordered environment.
From finite size scaling of both eigenvalue statistics and participation ratio,
we identify localization transitions in both the non-Hermitian Lindbladian
spectrum, which governs transient relaxation dynamics, and in the Hermitian
stationary state density matrix. These localization transitions occur at
different critical values of Hamiltonian and dissipative disorder strength,
implying the existence of atypical phases with a mixture of localized and
delocalized features. We find this phenomenon is robust to changes to the value
of the dissipative spectral gap.
