The new round of experiments, MEG II, COMET/Mu2e, and Mu3e, would soon start to push the $\mu \to e\gamma$, $\mu N\to eN$ conversion, and $\mu \to 3e$ frontier, while Belle II would probe $\tau \to \mu \gamma$ and $\tau \to 3\mu$. In the general two Higgs doublet model with extra Yukawa couplings, we show that all these processes probe the lepton flavor violating (LFV) dipole transition that arises from the two loop mechanism, with scalar-induced contact terms subdominant. This is because existing data suggest the extra Yukawa couplings ${\rho }_{\mu e},{\rho }_{ee}\lesssim {\lambda }_e$, while ${\rho }_{\tau \mu },{\rho }_{\tau \tau }\lesssim {\lambda }_{\tau }$ and ${\rho }_{tt}\lesssim {\lambda }_t$, with ${\lambda }_i$ the usual Yukawa coupling of the Standard Model (SM), where ${\rho }_{\mu e}{\rho }_{tt}$ and ${\rho }_{\tau \mu }{\rho }_{tt}$ enter the $\mu e\gamma$ and $\tau \mu \gamma$ two loop amplitudes, respectively. With the $B_s\to \mu \mu$ decay rate basically consistent with SM expectation, together with the $B_s$ mixing constraint, we show that $B_s\to \tau \tau$ would also be consistent with SM, while $B_s\to \tau \mu$ and $B\to K\tau \mu$ decays would be out of reach of projected sensitivities, in strong contrast with some models motivated by the B anomalies.