Two nights of phase-resolved medium resolution VLT spectroscopy of the extra-galactic low mass X-ray binary LMC X-2 have revealed a 0.32+/-0.02 day spectroscopic period in the radial velocity curve of the HeII lambda4686 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 disk in LMC X-2. This is strengthened by HeII lambda4686 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 LMC X-2,with a velocity of K_em=351+/-28 km/s, that we tentatively interpret as coming from the irradiated side of the donor star. Since K_em must be smaller than K_2, this leads to the first upper-limit on the mass function of LMC X-2 of f(M_1)>=0.86Msun (95% confidence), and the first constraints on its system parameters.
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