We carry on a new analysis of the sample of MACHO microlensing candidates towards the LMC. Our main purpose is to determine the lens population to which the events may belong. We give particular emphasis to the possibility of characterizing the Milky Way dark matter halo population with respect to the LMC one. Indeed, we show that only a fraction of the events have characteristics that match those expected for lenses belonging to the MACHO population of the Milky Way halo. This suggests that this component cannot explain all the candidates. Accordingly, we challenge the view that the dark matter halo fraction of both the Milky Way and the LMC halos are equal, and indeed we show that, for a MACHO mass in the range 0.1-0.3 M$_odot$, the LMC halo fraction can be significantly larger than the Milky Way one. In this perspective, our main conclusion is that up to about half of the observed events could be attributed to the LMC MACHO dark matter halo.