We report on the results of a $sim$40 d multi-wavelength monitoring of the Be X-ray binary system IGR J05007-7047 (LXP 38.55). During that period the system was monitored in the X-rays using the Swift telescope and in the optical with multiple instruments. When the X-ray luminosity exceeded $10^{36}$ erg/s we triggered an XMM-Newton ToO observation. Timing analysis of the photon events collected during the XMM-Newton observation reveals coherent X-ray pulsations with a period of 38.551(3) s (1 {sigma}), making it the 17$^{th}$ known high-mass X-ray binary pulsar in the LMC. During the outburst, the X-ray spectrum is fitted best with a model composed of an absorbed power law ($Gamma =0.63$) plus a high-temperature black-body (kT $sim$ 2 keV) component. By analysing $sim$12 yr of available OGLE optical data we derived a 30.776(5) d optical period, confirming the previously reported X-ray period of the system as its orbital period. During our X-ray monitoring the system showed limited optical variability while its IR flux varied in phase with the X-ray luminosity, which implies the presence of a disk-like component adding cooler light to the spectral energy distribution of the system.