  Two classes of far detectors have been proposed or are under operation at the
LHC. The first class is a series of neutrino detectors that are sensitive to
light active neutrinos via either charged-current or neutral-current
interactions; exemplary ideas are FASER$\nu$, SND@LHC, and FLArE. Another type
aims primarily at looking for displaced decays of long-lived particles (LLPs)
into charged final-state particles, including ANUBIS and FASER. In this work,
we propose searches for probing lepton number violation associated with a
Majorana active/sterile neutrino, for the first time with these experiments,
which, if discovered, would be a clear signature of new physics beyond the
Standard Model. With Monte-Carlo simulation, we find that while the neutrino
detectors, unfortunately, are estimated to have signal-event rates orders of
magnitude below $\mathcal{O}(1)$, some LLP far detectors such as ANUBIS, if
upgraded, would be most promising for discovering a Majorana sterile neutrino
of mass $\mathcal{O}(\text{1})$ GeV in certain so-far unexcluded parameter
space. In this exploratory work, we emphasize on the importance of leveraging
the LHC far detectors for purposes beyond the planned ones, such as searching
for lepton number violation.
