  We present a study of the evolutionary state of a few lithium-rich giant
stars based on the Gaia DR2 parallaxes and photometry. We also investigate the
chromospheric activity, the presence of a surface magnetic field, and the
radial velocity for our sample stars. We analysed both archive and new data. We
gathered archive spectra from several instruments, mainly ELODIE and NARVAL,
and we added new data acquired with the spectrograph MUSICOS. We applied the
Least-Squares Deconvolution technique to obtain Stokes V and Stokes I mean
profiles to compute longitudinal magnetic field for a subset. Moreover, for the
same subset, we analysed the Ca II H and K emission lines to calculate the
S-index. We also derived atmospheric parameters and Li abundances for all
eighteen stars of our sample. We found that stars previously classified as RGB
may actually be at a different evolutionary state. Furthermore, we identified
that most stars in our sample with detection of surface magnetic field show at
least moderate rotation velocities, but nonetheless, we could not detect a
magnetic field in two fast rotators. Due to our small sample of magnetic
giants, it is difficult to determine if the presence of surface magnetic field
and the Li-rich giant phenomena could be somehow linked. The large variation of
the radial velocity of part of our sample indicates that some of them might
have a binary companion, which may change the way we look at the Li problem in
giant stars.
