We present high-resolution optical echelle spectroscopy for a large fractio
n of the Li-rich late-type stars recently discovered in the vicinity of the
Lupus dark clouds. Our results confirm the high Li I lambda 6708 equivalen
t widths previously estimated from medium-resolution spectra, thus adding s
trength to the conclusion that the large majority of these stars are still
in the pre-main-sequence phase of their evolution, contrary to claims from
other authors that many of them might be zero-age main-sequence stars. We p
resent a statistical approach to derive a mean distance for the sample, and
find that it is consistent with, or slightly lower than, the Hipparcos dis
tance of the Lupus star-forming region. The radial velocities measured for
part of these stars are consistent with those observed for the Lupus star-f
orming region, while stars outside the dark clouds show a mean difference o
f the order of 3 km s(-1). The projected rotational velocities show a lack
of slow rotators, which is interpreted as a consequence of the X-ray select
ion of the sample. The Li-rich stars in Lupus studied in this work yield a
fairly 'clean' sample of very young stars, while in other star-forming regi
ons a larger fraction of older zero-age main-sequence stars has been found
among ROSAT-discovered Li-rich stars. We argue that this fact reflects the
relation of these stars with the Gould Belt.