  We analyze the most general dimension six effective Lagrangian, invariant
under the flavour symmetry A4 x Z3 x U(1) proposed to reproduce the near
tri-bimaximal lepton mixing observed in neutrino oscillations. The effective
Lagrangian includes four-lepton operators that violate the individual lepton
numbers in the limit of exact flavor symmetry and allow unsuppressed processes
satisfying the rule |Delta L_e x Delta L_mu x Delta L_tau| = 2. The most
stringent bounds on the strength of the new interactions come from the observed
universality of leptonic muon and tau decays, from the agreement between the
Fermi constant measured in the muon decay and that extracted from the mW/mZ
ratio, and from the limits on the rare decays tau^- -> mu^+ e^- e^- and tau^-
-> e^+ mu^- mu^-. We also investigate these effects in a specific
supersymmetric (SUSY) realization of the flavour symmetry and we find large
suppression factors for all the processes allowed by the selection rule. We
explain why this rule is violated in the SUSY context and we provide a complete
picture of lepton flavour violation in the SUSY version of A4 x Z_3 x U(1).
