  We calculate loop induced lepton flavor violating Higgs decays in the
Littlest Higgs model with T-parity. We find that a finite amplitude is obtained
only when all contributions from the T-odd lepton sector are included. This is
in contrast to lepton flavor violating processes mediated by gauge bosons where
the partners of the right-handed mirror leptons can be decoupled from the
spectrum. These partners are necessary to cancel the divergence in the Higgs
mass introduced by the mirror leptons but are otherwise unnecessary and assumed
to be decoupled in previous phenomenological studies. Furthermore, as we
emphasize, including the partner leptons in the spectrum also introduces a new
source of lepton flavor violation via their couplings to the physical
pseudo-Goldstone electroweak triplet scalar. Although this extra source also
affects lepton flavor changing gauge transitions, it decouples from these
amplitudes in the limit of heavy mass for the partner leptons. We find that the
corresponding Higgs branching ratio into taus and muons can be as large as
$\sim 0.2 \times 10^{-6}$ for T-odd masses of the order a few TeV, a demanding
challenge even for the high luminosity LHC.
