Domain wall nanoelectronics is a rapidly evolving field, which explores the diverse electronic properties of the ferroelectric domain walls for application in low-dimensional electronic systems. One of the most prominent features of the ferroelectric domain walls is their electrical conductivity. Here, using a combination of scanning probe and scanning transmission electron microscopy, the mechanism of the tunable conducting behavior of the domain walls in the sub-micrometer thick films of the technologically important ferroelectric LiNbO3 is explored. It is found that the electric bias generates stable domains with strongly inclined domain boundaries with the inclination angle reaching 20° with respect to the polar axis. The head-to-head domain boundaries exhibit high conductance, which can be modulated by application of the sub-coercive voltage. Electron microscopy visualization of the electrically written domains and piezoresponse force microscopy imaging of the very same domains reveals that the gradual and reversible transition between the conducting and insulating states of the domain walls results from the electrically induced wall bending near the sample surface. The observed modulation of the wall conductance is corroborated by the phase-field modeling. The results open a possibility for exploiting the conducting domain walls as the electrically controllable functional elements in the multilevel logic nanoelectronics devices.