Context : 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 .

Aims : We aim at unveiling the nature of the Galactic DCEP V363 Cas and other DCEPs showing cosmic abundances of lithium in their atmospheres .

Methods : We have collected three epochs high-resolution spectroscopy for V363 Cas with HARPS-N @ TNG .
Accurate stellar parameters : effective temperatures , gravities , microturbulences , radial velocities , and metal abundances were measured for this star .

Results : We detected a lithium abundance of A ( Li ) = 2.86 \pm 0.10 dex , along with iron , carbon and oxygen abundances of [ Fe/H ] = - 0.30 \pm 0.12 dex , [ C/H ] = - 0.06 \pm 0.15 dex and [ O/H ] = 0.00 \pm 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 .

Conclusions : 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 .