Two nights of phase-resolved medium-resolution Very Large Telescope spectroscopy of the extra-galactic low-mass X-ray binary LMCX-2 have revealed a 0.32 +/- 0.02 d spectroscopic period in the radial velocity curve of the HeII λ4686 emission line that we interpret as the orbital period. However, similar to previous findings, this radial velocity curve shows a longer term variation that is most likely due to the presence of a precessing accretion disc in LMCX-2. This is strengthened by HeII λ4686 Doppler maps that show a bright spot that is moving from night to night. Furthermore, we detect narrow emission lines in the Bowen region of LMCX-2, with a velocity of Kem = 351 +/- 28 km s-1, that we tentatively interpret as coming from the irradiated side of the donor star. Since Kem must be smaller than K2, this leads to the first upper limit on the mass function of LMCX-2 of f(M1) >= 0.86 Msolar (95 per cent confidence), and the first constraints on its system parameters.