Interfacial 'dead' layers between metals and ferroelectric thin films generally induce detrimental effects in nanocapacitors, yet their peculiar properties can prove advantageous in other electronic devices. Here, we show that dead layers with low Li concentration located at the surface of LiNbO3 ferroelectric materials can function as unipolar selectors. LiNbO3 mesa cells were etched from a single-crystal LiNbO3 substrate, and Pt metal contacts were deposited on their sides. Poling induced non-volatile switching of ferroelectric domains in the cell, and volatile switching in the domains in the interfacial (dead) layers, with the domain walls created within the substrate being electrically conductive. These features were also confirmed using single-crystal LiNbO3 thin films bonded to SiO2/Si wafers. The fabricated nanoscale mesa-structured memory cell with an embedded interfacial-layer selector shows a high on-to-off ratio (>106) and high switching endurance (~1010 cycles), showing potential for the fabrication of crossbar arrays of ferroelectric domain wall memories.