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.
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