We present the results of a large spectroscopic survey of the LMC, consisting of more than 1300 radial velocities measured accurately with the 2dF instrument during three observing compaigns 1999-2002. In this sample, no evidence is found for any extraneous, kinematically distinct population over the expected LMC and Galactic components. We discuss the significance of this finding for the LMC self-lensing models. The sample was randomly selected from three APM photographic plates with 16<=R<=18mag and -1.0<=Bj-R<=2.5mag. The fields were centered on previous microlensing events. The 1200V grating was used with 1.1{AA} per pixel resolution over 4625-5765{AA}. The zero point of the velocity of LMC K-type stars is set by cross-correlating with a K-type standard star. For sample stars of other spectral type we assume no systematic change of the peak of velocity distribution with spectral type.