Submitted on 4 Mar 2008 (v1), last revised 2 Jul 2008 (this version, v2).-- Section on μ-e conversion in nuclei added, version to appear in PRD.In the framework of the seesaw models with triplets of fermions, we evaluate the decay rates of μ --> eγ and τ --> lγ transitions. We show that although, due to neutrino mass constraints, those rates are in general expected to be well under the present experimental limits, this is not necessarily always the case. Interestingly enough, the observation of one of those decays in planned experiments would nevertheless contradict bounds stemming from present experimental limits on the μ --> eee and τ --> 3l decay rates. Such detection of radiative decays would therefore imply that there exist sources of lepton flavour violation not associated to triplet fermions.The authors received partial support from CICYT through the project FPA2006-05423, as well as from the Comunidad Autónoma de Madrid through Proyecto HEPHACOS; P-ESP-00346. T.H. thanks the FNRS-FRS for support. A.A and F.B acknowledge the support of the Agence Nationale de la Recherche ANR through the project JC05-43009-NEUPAC.Peer reviewed