LiCu_{3}O_{3} is an antiferromagnetic mixed valence cuprate where trilayers of edge-sharing Cu(II)O (3d^{9}) are sandwiched in between planes of Cu(I) (3d^{10}) ions, with Li stochastically substituting Cu(II). Angle-resolved photoemission spectroscopy (ARPES) and density functional theory reveal two insulating electronic subsystems that are segregated in spite of sharing common oxygen atoms: a Cu d_{z^{2}}/O p_{z} derived valence band (VB) dispersing on the Cu(I) plane, and a Cu 3d_{x^{2}-y^{2}}/O 2p_{x,y} derived Zhang-Rice singlet (ZRS) band dispersing on the Cu(II)O planes. First-principle analysis shows the Li substitution to stabilize the insulating ground state, but only if antiferromagnetic correlations are present. Li further induces substitutional disorder and a 2D electron glass behavior in charge transport, reflected in a large 530meV Coulomb gap and a linear suppression of VB spectral weight at E_{F} that is observed by ARPES. Surprisingly, the disorder leaves the Cu(II)-derived ZRS largely unaffected. This indicates a local segregation of Li and Cu atoms onto the two separate corner-sharing Cu(II)O_{2} sub-lattices of the edge-sharing Cu(II)O planes, and highlights the ubiquitous resilience of the entangled two hole ZRS entity against impurity scattering.