LiCu3O3 is an antiferromagnetic mixed valence cuprate where trilayers of edge -sharing Cu(II)O (3d9) are sandwiched in between planes of Cu(I) (3d10) 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 dz2/O pz derived valence band (VB) dispersing on the Cu(I) plane, and a Cu 3dx2-y2/O 2px,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 530 meV Coulomb gap and a linear suppression of VB spectral weight at EF 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 CuoII thorn O2 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.