  The LHC has recently reported a slight excess in the $h\rightarrow \tau \mu$
channel. If this lepton flavor violating (LFV) decay is confirmed, an extension
of the Standard Model (SM) will be required to explain it. In this paper we
investigate two different possibilities to accommodate such a LFV process: the
first scenario is based on flavor off-diagonal $A$-terms in the Minimal
Supersymmetric Standard Model (MSSM), and the second is a model where the Higgs
couples to new vectorlike fermions that couple to the SM leptons through a LFV
four fermion interaction. In the supersymmetric model, we find that the sizes
of the $A$-terms needed to accommodate the $h\rightarrow \tau\mu$ excess are in
conflict with charge- and color-breaking vacuum constraints. In the second
model, the excess can be successfully explained while satisfying all other
flavor constrains, with order one couplings, vectorlike fermion masses as low
as 15 TeV, and a UV scale higher than 35 TeV.
