We construct a semiclassical phase-space density of Schur vectors in non-Hermitian quantum systems. Each Schur vector is associated to a single Planck cell. The Schur states are organized according to a classical norm landscape on phase space-a classical manifestation of the lifetimes which are characteristic of non-Hermitian systems. To demonstrate the generality of this construction we apply it to a highly nontrivial example: a PT-symmetric kicked rotor in the regimes of mixed and chaotic classical dynamics.