  We analyze the sensitivity of next-generation tonne-scale neutrinoless double
$\beta$-decay ($0\nu\beta\beta$) experiments and searches for same-sign
di-electrons plus jets at the Large Hadron Collider to TeV scale lepton number
violating interactions. Taking into account previously unaccounted for physics
and detector backgrounds at the LHC, renormalization group evolution, and
long-range contributions to $0\nu\beta\beta$ nuclear matrix elements, we find
that the reach of tonne-scale $0\nu\beta\beta$ generally exceeds that of the
LHC. However, for a range of heavy particle masses near the TeV scale, the high
luminosity LHC and tonne-scale $0\nu\beta\beta$ may provide complementary
probes.
