A popular framework for exploring Lorentz violation is the Standard Model extension. This extension contains a large number of parameters that can be bounded in various experiments. Most studies, however, focus on the fermion or photon sector. Here, we consider Lorentz violation in the weak vector boson sector. The strongest bounds come from measurements of the asymmetry in Møller scattering. We study the bounds that can be obtained from future measurements of the parity violating asymmetry in deep inelastic electron-proton scattering at the EIC, the LHeC, and the FCC-eh. For the FCC-eh, the bounds could be substantially improved over current bounds by including timing information.