The definition for the "lowest unoccupied natural orbital" comes straight from the independent particle level of theory. In Hartree-Fock and DFT, the occupation numbers of the spin-orbitals are either 1 (occupied) or 0 (unoccupied). The highest occupied molecular orbital (HOMO) is the last orbital, ordered in orbital energy, which is occupied, and the lowest unoccupied MO (LUMO) is the first unoccupied one.

When you go to the post-HF level of theory, the wave function is no longer a single-particle one, as you include many configurations, and the reduced one-particle density matrix becomes non-diagonal in the Hartree-Fock orbital basis.

As you diagonalize the reduced one-particle density matrix, you get the natural orbitals (NOs) and their occupation numbers (NOONs). The HONO and LUNO are simply defined by the number of electrons you have: if the Nth and N+1:th orbitals are the HOMO and LUMO in Hartree-Fock, respectively, then the Nth and N+1:th NOs (ordered in decreasing occupation number) are the HONO and LUNO, respectively.