M^+M'^-$[@belle-tau-lMM; @babar-tau-lMM], $\tau \rightarrow \ell_i\ell'^+\ell'^-$[@belle-tau-3l; @babar-tau-3l], and $\tau \rightarrow \ell_i\gamma$[@belle-tau-egamma; @belle-tau-mugamma; @babar-tau-mugamma], where $\ell_i$ ($i=1,2$) respectively represent an electron and a muon, $P^0$ does $\pi^0$, $\eta$ and $\eta'$ mesons, $M^\pm$ ($M'^\pm$) does $\pi^\pm$ and $K^\pm$ mesons, and $\ell'^\pm=e^\pm$ and $\mu^\pm$. The LFV Yukawa couplings can be constrained from the data for these processes especially those with the Higgs boson mediation. For $\mu$-$e$ mixing, the Higgs boson mediated LFV coupling has been discussed in Ref. [@KitanoKoikeKomineOkada; @muegamma-type3THDM]. Tau lepton associated LFV processes with the Higgs boson mediation have been discussed in models with supersymmetry (SUSY)[@BK; @DER; @Sher-tmeta; @Rossi] as well as in the two Higgs doublet model (THDM) in some specific scenarios[@cheng-sher; @HiggsLFV-THDM; @Iltan]. In Ref. [@BHHS], tau associated LFV processes have been discussed comprehensively in the framework of 4-Fermi contact interactions. Phenomenological consequences of the LFV Yukawa couplings associated with tau leptons have also been studied for future observables such as $B_s$ decays[@bsmutau; @DER] at (super) B factories[@super-B] and Higgs boson decays[@Pilaftsis; @Rossi; @Herrero; @kot] at CERN LHC[@Assamagan], an electron-positron linear collider (LC)[@Osaka] and a muon collider[@muon-collider]. Furthermore, deep inelastic scattering processes $\mu N \to \tau X$[@Sher-turan; @mutauDIS] from intense high energy muons at neutrino factories (or muon colliders) and 