  New gauge bosons coupling to leptons are simple and well-motivated extensions
of the Standard Model. We study the sensitivity to gauged $L_{\mu} -L_{e}$,
$L_e-L_\tau$ and $L_{\mu} -L_{\tau}$ both with the existing beam dump mode data
of MiniBooNE and with the DUNE near detector. We find that including
bremsstrahlung and resonant production of $Z'$ which decays to $e^{\pm}$ and
$\mu^{\pm}$ final states leads to a significant improvement in existing bounds,
especially for $L_\mu-L_e$ and $L_e-L_\tau$ for DUNE while competitive
constraints can be achieved with the existing data from the MiniBooNE's beam
dump run.
