  We study the impact of heavy vector-like leptons on several observables in
collider and low-energy physics. These states, present in many well-motivated
extensions of the Standard Model, can induce lepton flavour violation and
non-standard Higgs decays. We study these effects in an effective model
inspired by the composite Higgs scenario. After deriving bounds on the mass and
production cross-section of the vector-like states using recent LHC data on
multilepton searches, we discuss the modification of the Higgs decays to
dilepton, diphoton and $Z\gamma$ final states as well as low-energy observables
like radiative lepton decays, the anomalous magnetic moment of the muon and the
electric dipole moment of the electron. We find several interesting
correlations. In particular, we show that branching fractions of lepton
flavour-violating Higgs decays at an observable level are prohibited due to the
strong bounds on the radiative lepton decays.
