  The number of known Be/X-ray binaries in the Large Magellanic Cloud is small
compared to the observed population of the Galaxy or the Small Magellanic
Cloud. The discovery of a system in outburst provides the rare opportunity to
measure its X-ray properties in detail. IGR J05414-6858 was discovered in 2010
by INTEGRAL and found in another outburst with the Swift satellite in 2011. In
order to characterise the system, we analysed the data from a follow-up
XMM-Newton target of opportunity observation of the 2011 outburst and
investigate the stellar counterpart with photometry and spectroscopy. We
modelled the X-ray spectra from the EPIC instruments on XMM-Newton and compared
them with Swift archival data. In the X-ray and optical light curves, we
searched for periodicities and variability. The optical counterpart was
classified using spectroscopy obtained with ESO's Faint Object Spectrograph at
NTT. The X-ray spectra as seen in 2011 are relatively hard with a photon index
of ~0.3-0.4 and show only low absorption. They deviate significantly from
earlier spectra of a probable type II outburst in 2010. The neutron star spin
period of P_s = 4.4208 s was discovered with EPIC-pn. The I-band light curve
revealed a transition from a low to a high state around MJD 54500. The optical
counterpart is classified to B0-1IIIe and shows Halpha emission and a variable
NIR excess, vanishing during the 2010 outburst. In the optical high state, we
found a periodicity at 19.9 days, probably caused by binarity and indicating
the orbital period.
