  We propose a radial velocity survey with the aim to resolve the current
dispute on the LMC lensing: in the pro-macho hypothesis the lenses are halo
white dwarfs or machos in general; in the pro-star hypothesis both the lenses
and the sources are stars in various observed or hypothesized structures of the
Magellanic Clouds and the Galaxy. Star-star lensing should prefer sources at
the backside or behind the LMC disc because lensing is most efficient if the
source is located a few kpc behind a dense screen of stars, here the thin disc
of the LMC. This signature of self-lensing can be looked for by a radial
velocity survey since kinematics of the stars at the back can be markedly
different from that of the majority of stars in the cold, rapidly rotating disc
of the LMC. Detailed simulations of effect together with optimal strategies of
carrying out the proposed survey are reported here. Assuming that the existing
30 or so alerted stars in the LMC are truely microlensed stars, their
kinematics can test the two lensing scenarios; the confidence level varies with
the still very uncertain structure of the LMC. Spectroscopy of the existing
sample and future events requires about two or three good-seeing nights per
year at a 4m-8m class southern telescope, either during the amplification phase
or long after.
