  Recent anomalies in the decays of $B$ mesons and the Higgs boson provide
hints towards lepton flavor (universality) violating physics beyond the
Standard Model. We observe that four-fermion operators which can explain the
$B$-physics anomalies have corresponding analogs in the kaon sector, and we
analyze their impact on $K\to\pi\ell \ell'$ and $K\to\ell \ell'$ decays
$(\ell=\mu,e)$. For these processes, we note the corresponding physics
opportunities at the NA62 experiment. In particular, assuming minimal flavor
violation, we comment on the required improvements in sensitivity necessary to
test the $B$-physics anomalies in the kaon sector.
