We point out that extensions of the standard model with low scale (approximately TeV) lepton number violation (LNV) generally lead to a pattern of lepton flavor violation (LFV) experimentally distinguishable from the one implied by models with grand unified theory scale LNV. As a consequence, muon LFV processes provide a powerful diagnostic tool to determine whether or not the effective neutrino mass can be deduced from the rate of neutrinoless double beta decay. We discuss the role of mu-->egamma and mu-->e conversion in nuclei, which will be studied with high sensitivity in forthcoming experiments.