  The experimental value of the anomalous magnetic moment of the muon, as well
as the LHCb anomalies, point towards new physics coupled non-universally to
muons and electrons. Working in extra dimensional theories, which solve the
electroweak hierarchy problem with a warped metric, strongly deformed with
respect to the AdS$_5$ geometry at the infra-red brane, the LHCb anomalies can
be solved by imposing that the bottom and the muon have a sizable amount of
compositeness, while the electron is mainly elementary. Using this set-up as
starting point we have proven that extra physics has to be introduced to
describe the anomalous magnetic moment of the muon. We have proven that this
job is done by a set of vector-like leptons, mixed with the physical muon
through Yukawa interactions, and with a high degree of compositeness. The
theory is consistent with all electroweak indirect, direct and theoretical
constraints, the most sensitive ones being the modification of the
$Z\bar\mu\mu$ coupling, oblique observables and constraints on the stability of
the electroweak minimum. They impose lower bounds on the compositeness
($c\lesssim 0.37$) and on the mass of the lightest vector-like lepton ($\gtrsim
270$ GeV). Vector-like leptons could be easily produced in Drell-Yan processes
at the LHC and detected at $\sqrt{s}=13$ TeV.
