The observation of neutrino oscillations and masses motivates the extension of the standard model with right handed neutrinos, leading to heavy neutrino states possibly in the electroweak scale, which could be impacted by new high-scale weakly coupled physics. A systematic tool for studying these interactions is the neutrino-extended standard model effective field theory νSMEFT. In this work we study the prospects of the future LHeC electron-proton collider to discover or constrain the νSMEFT interactions, performing the first dedicated and realistic analysis of the well known lepton-trijet signals, both for the lepton flavor violating p e− → µ − + 3j (LFV) and the lepton number violating p e− → µ + + 3j (LNV) channels, for HNLs masses in the electroweak scale range: 100 GeV ≤ mN ≤ 500 GeV. The obtained sensitivity prospects show that the LHeC with 100 fb−1 luminosity could be able to probe the scenario of a heavy N and constrain the effective couplings to a region of the parameter space as tight as the bounds that are currently considered for the O(10) GeV scale masses, with effective couplings of O(10−1) for NP scale Λ = 1TeV.