  Classical Cepheids (DCEPs) are important astrophysical objects not only as
standard candles for the determination of the cosmic distance ladder but also
as a test-bed for the stellar evolution theory, thanks to the connection
between their pulsation (periods, amplitudes) and stellar (luminosity, mass,
effective temperature, metallicity) parameters. We aim to unveil the nature of
the Galactic DCEP OGLE-GD-CEP-0516 and other DCEPs showing an enhanced
abundance of lithium in their atmospheres. We have collected a high-resolution
spectrum for OGLE-GD-CEP-0516 with UVES@VLT. Accurate stellar parameters:
effective temperature, gravity, micro- and macro-turbulence, radial velocity,
and metal abundances were measured for this star, using spectral synthesis
techniques based on LTE plane-parallel atmospheric model. We measured a
chemical pattern with most elements under-abundant compared with the Sun, i.e.
[Fe/H]\,=\,$-$0.54\,$\pm$\,0.16~dex, [C/H]\,=\,$-$0.45\,$\pm$\,0.05~dex, or
[Mg/H]\,=\,$-$0.40\,$\pm$\,0.16~dex among others. In particular, we measured a
lithium abundance A(Li)\,=\,3.06\,$\pm$\,0.10~dex for OGLE-GD-CEP-0516, which
makes this object the sixth Li-rich object among the Milky Way DCEPs. Our
results favour the scenario in which the six Galactic Li-rich DCEPs are
first-crossing the instability strip having had slowly-rotating progenitors
during their main sequence phase. This study explored the link between lithium
abundance and the pulsation period in classical Cepheids. It found that
brighter Cepheids, indicative of higher mass, show enhanced lithium abundance,
contrary to predictions from evolutionary models considering rotation.
Additionally, an analysis of lithium abundance versus [Fe/H] revealed a lack of
significant correlation, contradicting expectations from galactic chemical
evolution (GCE) models.
