  The possibility that the 125 GeV Higgs boson may decay into invisible
non-standard-model (non-SM) particles is theoretically and phenomenologically
intriguing. In this letter we investigate the sensitivity of the Large Hadron
Electron Collider (LHeC) to an invisibly decaying Higgs, in its proposed high
luminosity running mode. We focus on the neutral current Higgs production
channel which offers more kinematical handles than its charged current
counterpart. The signal contains one electron, one jet and large missing
energy. With a cut-based parton level analysis, we estimate that if the $hZZ$
coupling is at its standard model (SM) value, then assuming an integrated
luminosity of $1\,\mbox{ab}^{-1}$ the LHeC with the proposed 60 GeV electron
beam (with $-0.9$ polarization) and 7 TeV proton beam is capable of probing
$\mathrm{Br}(h\rightarrow E\!\!\!\!/_T)=6\%$ at $2\sigma$ level. Good lepton
veto performance (especially hadronic $\tau$ veto) in the forward region is
crucial to the suppression of the dominant $Wje$ background. We also explicitly
point out the important role that may be played by the LHeC in probing a wide
class of exotic Higgs decay processes and emphasize the general function of
lepton-hadron colliders in precision study of new resonances after their
discovery in hadron-hadron collisions.
