  Within the framework of the $\mu\nu$SSM, a displaced dilepton signal is
expected at the LHC from the decay of a tau left sneutrino as the lightest
supersymmetric particle (LSP) with a mass in the range $45 - 100$ GeV. We
compare the predictions of this scenario with the ATLAS search for long-lived
particles using displaced lepton pairs in $pp$ collisions, considering an
optimization of the trigger requirements by means of a high level trigger that
exploits tracker information. The analysis is carried out in the general case
of three families of right-handed neutrino superfields, where all the neutrinos
get contributions to their masses at tree level. To analyze the parameter
space, we sample the $\mu\nu$SSM for a tau left sneutrino LSP with proper decay
length $c\tau > 0.1$ mm using a likelihood data-driven method, and paying
special attention to reproduce the current experimental data on neutrino and
Higgs physics, as well as flavor observables. The sneutrino is special in the
$\mu\nu$SSM since its couplings have to be chosen so that the neutrino
oscillation data are reproduced. We find that important regions of the
parameter space can be probed at the LHC run 3.
