We have used high-voltage Kelvin Probe Force Microscopy to map the spatial distribution of electrical potential, dropped along curved current-carrying conducting domain walls, in x-cut single crystal ferroelectric lithium niobate thin films. We find that in-operando potential profiles and extracted electric fields, associated with p-n junctions contained within the walls, can be fully rationalised through expected variations in wall resistivity alone. There is no need to invoke additional physics (carrier depletion zones, space-charge fields) normally associated with extrinsically doped semiconductor p-n junctions. Indeed, we argue that this should not even be expected, as inherent Fermi level differences between p- and n- regions, at the core of conventional p-n junction behaviour, cannot occur in domain walls that are surrounded by a common matrix. This is important for domain wall nanoelectronics, as such in-wall junctions will neither act as diodes nor facilitate transistors in the same way as extrinsic semiconducting systems do.