  We analyze a displaced dilepton signal expected at the LHC for a tau left
sneutrino as the lightest supersymmetric particle with a mass in the range
$45$-$100$ GeV. The sneutrinos are pair produced via a virtual $W$, $Z$ or
$\gamma$ in the $s$ channel and, given the large value of the tau Yukawa
coupling, their decays into two dileptons or a dilepton plus missing transverse
energy from neutrinos can be significant. The discussion is carried out in the
$\mu \nu$SSM, where the presence of $R$-parity violating couplings involving
right-handed neutrinos solves the $\mu$ problem and can reproduce the neutrino
data. To probe the tau left sneutrinos we compare the predictions of the $\mu
\nu$SSM with the ATLAS search for long-lived particles using displaced lepton
pairs in $pp$ collisions at $\sqrt s= 8$ TeV, allowing us to constrain the
parameter space of the model. We also consider an optimization of the trigger
requirements used in existing displaced-vertex searches by means of a High
Level Trigger that exploits tracker information. This optimization is
generically useful for a light metastable particle decaying into soft charged
leptons. The constraints on the sneutrino turn out to be more stringent. We
finally discuss the prospects for the $13$ TeV LHC searches as well as further
potential optimizations.
