  In the framework of microlensing searches towards the Large Magellanic Cloud
(LMC), we discuss the results presented by the OGLE collaboration for their
OGLE-II campaign \citep{lukas09}. We evaluate the optical depth, the duration
and the expected rate of events for the different possible lens populations:
both luminous, dominated by the LMC self lensing, and "dark", the would be
compact halo objects (MACHOs) belonging to either the Galactic or to the LMC
halo. The OGLE-II observational results, 2 microlensing candidate events
located in the LMC bar region with duration of 24.2 and 57.2 days, compare well
with the expected signal from the luminous lens populations:
$n_\mathrm{exp}=1.5$, with typical duration, for LMC self lensing, of about 50
days. Because of the small statistics at disposal, however, the conclusions
that can be drawn as for the halo mass fraction, $f$, in form of compact halo
objects are not too severe. By means of a likelihood analysis we find an
\emph{upper} limit for $f$, at 95% confidence level, of about 15% in the mass
range $(10^{-2}-10^{-1}) \mathrm{M}_\odot$ and 26% for $0.5 \mathrm{M}_\odot$.
