Conductive domain walls (DWs) in insulating ferroelectrics have recently attracted considerable attention due to their unique topological, optical, and electronic properties, and offer potential applications such as in memory devices or rewritable circuitry. The electronic properties of DWs can be tuned by the application of strain, hence controlling the charge carrier density at DWs. In this paper, we study the influence of uniaxial stress on the conductivity of DWs in the bulk single crystal lithium niobate (LiNbO3). Using conductive atomic force microscopy, we observe a large asymmetry in the conductivity of DWs, where only negatively screened walls, so called head-to-head DWs, are becoming increasingly conductive, while positively screened, tail-to-tails DWs, show a decrease in conductivity. This asymmetry of DW conductivity agrees with our theoretical model based on the piezoelectric effect. In addition, we observed that the current in the DW increases up to an order of magnitude for smaller compressive stresses of 100 MPa. This response of DWs remained intact for multiple stress cycles over two months, opening a path for future applications.