  The Large Hadron electron Collider (LHeC) has been designed to push the field
of deep inelastic scattering to the high energy and intensity frontier using an
intense electron beam with a proton beam from the High Luminosity-Large Hadron
Collider. However, LHeC is also a great laboratory for new physics. In this
work, we propose a search for dark matter that couples with leptons. This may
yield $ej$+ missing energy and $\mu j$ + missing energy signals that can be
potentially observed through simple missing-energy cuts that suppress the
Standard Model background. Considering direct dark matter detection and LHC
constraints, we show that LHeC can indeed discover a weak scale dark matter
fermion for masses up to 350 GeV, which reproduces the correct relic density,
and has interesting implications for lepton flavor violation.
