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.
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