  We consider the $A_4$, $S_4$ and $A_5$ discrete lepton flavour symmetries in
the case of 3-neutrino mixing, broken down to non-trivial residual symmetries
in the charged lepton and neutrino sectors in such a way that at least one of
them is a $Z_2$. Such symmetry breaking patterns lead to predictions for some
of the three neutrino mixing angles and/or the leptonic Dirac CP violation
phase $\delta$ of the neutrino mixing matrix. We assess the viability of these
predictions by performing a statistical analysis which uses as an input the
latest global data on the neutrino mixing parameters. We find 14
phenomenologically viable cases providing distinct predictions for some of the
mixing angles and/or the Dirac phase $\delta$. Employing the current best fit
values of the three neutrino mixing angles, we perform a statistical analysis
of these cases taking into account the prospective uncertainties in the
determination of the mixing angles, planned to be achieved in currently running
(Daya Bay) and the next generation (JUNO, T2HK, DUNE) of neutrino oscillation
experiments. We find that only six cases would be compatible with these
prospective data. We show that this number is likely to be further reduced by a
precision measurement of $\delta$.
