  The determination of the Higgs self coupling is one of the key ingredients
for understanding the mechanism behind the electroweak symmetry breaking. An
indirect method for constraining the Higgs trilinear self coupling via single
Higgs production at next-to-leading order (NLO) has been proposed in order to
avoid the drawbacks of studies with double Higgs production. In this paper we
study the Higgs self interaction through the vector boson fusion (VBF) process
$e^{-} p \to \nu_{e} h j$ at the future LHeC. At NLO level, we compute
analytically the scattering amplitudes for relevant processes, in particular
those induced by the Higgs self interaction. A Monte Carlo simulation and a
statistical analysis utilizing the analytic results are then carried out for
Higgs production through VBF and decay to $b\bar{b}$, which yield for the
trilinear Higgs self-coupling rescaling parameter $\kappa_{\lambda}$ the limit
[-0.57, 2.98] with $2~\text{ab}^{-1}$ integrated luminosity. If we assume about
10% of the signal survives the event selection cuts, and include all the
background, the constraint will be broadened to [-2.11, 4.63].
