  We study leptons in holographic composite Higgs models, namely in models
possibly admitting a weakly coupled description in terms of five-dimensional
(5D) theories. We introduce two scenarios leading to Majorana or Dirac
neutrinos, based on the non-abelian discrete group $S_4\times \Z_3$ which is
responsible for nearly tri-bimaximal lepton mixing. The smallness of neutrino
masses is naturally explained and normal/inverted mass ordering can be
accommodated. We analyze two specific 5D gauge-Higgs unification models in
warped space as concrete examples of our framework. Both models pass the
current bounds on Lepton Flavour Violation (LFV) processes. We pay special
attention to the effect of so called boundary kinetic terms that are the
dominant source of LFV. The model with Majorana neutrinos is compatible with a
Kaluza-Klein vector mass scale $m_{KK}\gtrsim 3.5$ TeV, which is roughly the
lowest scale allowed by electroweak considerations. The model with Dirac
neutrinos, although not considerably constrained by LFV processes and data on
lepton mixing, suffers from a too large deviation of the neutrino coupling to
the $Z$ boson from its Standard Model value, pushing $m_{KK}\gtrsim 10$ TeV.
