  In this paper we consider a plausible scenario with conserved lepton number
\textbf{$L=L_{e}-L_{\mu}-L_{\tau}$} within the framework of the exact solution
of a particular 3-3-1 gauge model. We discuss what are the consequences of
conserving this global leptonic symmetry from the viewpoint of the neutrino
mass matrix constructed via special Yukawa terms (involving tensor products
among Higgs triplets). We prove that the actual experimental data can naturally
be reproduced by our scenario since soft breaking terms with respect to this
lepton symmetry are properly introduced. As a consequence, our solution
predicts for the neutrino sector the correct mass splitting ratio ($\Delta
m_{12}^{2}/\Delta m_{23}^{2}\simeq0.033$), the inverted mass hierarchy, the
correct values for the observed mixing angles ($\sin^{2}\theta_{23}\simeq0.5$
and $\sin^{2}\theta_{12}=0.31$)and the absolute mass of the lightest neutrino
($m_{0}\sim0.001$eV)independent of the breakung scale of the model.
