  The aim of this work is to search for Li-rich giants in a sample of clusters
where planets have been searched, thus we can study the planet engulfment
scenario to explain Li replenishment using a proper comparison sample of stars
without detected giant planets. We derived Li abundances for a sample of 67 red
giant stars in 12 different open clusters using standard spectral synthesis
techniques and high resolution spectra (from HARPS and UVES). We also
determined masses, ages and radius from PARSEC stellar isochrones to constrain
the evolutionary stage of these stars. We find three stars in different
clusters with clearly enhanced Li abundances compared to other stars within the
cluster. Interestingly, the only two stars with a detected substellar companion
in our sample belong to that group. One of the planet hosts, NGC2423No3, might
lie close to the luminosity bump on the HR diagram, a phase where Li production
by the Cameron-Fowler process is supported by extra-mixing to bring fresh Li up
to the surface. On the other hand, NGC4349No127 is a more massive and more
evolved giant that does not seem to be in the evolutionary phase where other
Li-rich stars are found. We discuss the possibility that the Li enhancement of
this star is triggered by the engulfment of a planet, considering that close-in
planets hardly survive the RGB-tip and the early-AGB phases.
