We present in full analytic form the partial widths for the lepton flavour violating decays $L^\pm \to \ell^\pm \ell'^{+} \ell'^{-}$, with $L = \tau, \mu$ and $\ell(') = \mu, e$, mediated by neutrino oscillations in the one-loop diagrams. Compared to the first result by Petcov:1976ff, which was obtained in the nonphysical zero momentum limit $\mathcal{P} \ll m_{\nu} \ll M_W$, we retain full dependence on external scales $\mathcal{P}$ and determine the branching ratios in the physical limit $m_\nu \ll \mathcal{P} \ll M_W$. We show that in this limit the conclusion by Pham:1998fq that $\tau \to \ell \ell' \ell'$ could be as large as $10^{-14}$ is flawed. In this talk we will describe the details of our calculation, present our results, and motivate some of the peculiarities of this calculation from the viewpoint of effective field theory.