  Classical Cepheids (DCEPs) are important astrophysical objects not only as
standard candles in the determination of the cosmic distance ladder, but also
as a testbed for the stellar evolution theory, thanks to the strict connection
between their pulsation [period(s), amplitudes] and stellar (luminosity, mass,
effective temperature, metallicity) parameters. We aim at unveiling the nature
of the Galactic DCEP V363 Cas and other DCEPs showing cosmic abundances of
lithium in their atmospheres. We have collected three epochs high-resolution
spectroscopy for V363 Cas with HARPS-N@TNG. Accurate stellar parameters:
effective temperatures, gravities, micro-turbulences, radial velocities, and
metal abundances were measured for this star. We detected a lithium abundance
of A(Li)=2.86+-0.10 dex, along with iron, carbon and oxygen abundances of
[Fe/H]=-0.30+-0.12 dex, [C/H]=-0.06+-0.15 dex and [O/H]=0.00+-0.12 dex. V363
Cas is the fifth among the Milky Way DCEPs to exhibit a Li-rich feature. An
analysis of historical time-series spanning a hundred year interval shows that
the period of V363 Cas is increasing, with a sharp acceleration after
HJD=2453000. This is a clear hint of first crossing of the instability strip.
Our results favour the scenario in which the five Galactic Li-rich DCEPs are
first-crossing the instability strip having had slowly-rotating progenitors
during their main sequence phase.
