  We study lepton flavor violating (LFV) $B$ decays in a general two Higgs
doublet model with sub-TeV exotic scalars. Two different parameter spaces are
explored: one dominated by extra top Yukawa coupling $\rho_{tt}$, the other by
LFV couplings relevant for the muon $g-2$ anomaly. In the first case, flavor
constraints such as $\ell \to \ell^\prime\gamma$, $h \to \ell\ell^\prime$ imply
LFV $B$ decays are far below experimental sensitivities. The second case needs
to be close to the alignment limit, but $B_q \to \tau\mu$ and $B \to (K, \pi)
\tau\mu$ rates can lie within the sensitivities of Belle II and LHCb Upgrade
II. Neutral $B$ meson mixings and $B,\, K,\, \pi \to \ell \nu$ decays provide
important flavor constraints on parameter space. $B$ decays involving
$e$-$\tau$ violation are constrained by $\mu\to e$ processes.
