  Majorana neutrinos in the seesaw model can have sizable mixings through which
they can be produced at the Large Hadron Collider (LHC) and show a remarkable
Lepton Number Violating (LNV) signature. In this article we study the LNV decay
of the W boson via two almost degenerate heavy on-shell Majorana neutrinos
$N_j$, into three charged leptons and a light neutrino. We consider the
scenario where the heavy neutrino masses are within $1$ GeV $\leq M_N \leq 10$
GeV. We evaluated the possibility to measure a LNV oscillation process in such
a scenario, namely, the modulation of the quantity $d \Gamma/d L$ for the
process at the LHC where $W^{\pm} \to \mu^{\pm} N \to \mu^{\pm} \tau^{\pm}
W^{\mp *}$ $ \to \mu^{\pm} \tau^{\pm} e^{\mp} \nu_e$. $L$ is the distance
within the detector between the two vertices of the process. We found out some
realistic conditions under which such a modulation could be probed at the LHC.
