Context :

Aims : We report 20 new lithium-rich giants discovered within the Gaia -ESO Survey , including the first Li-rich giant with an evolutionary stage confirmed by CoRoT ( Convection , Rotation and planetary Transits ) data .
We present a detailed overview of the properties of these 20 stars .

Methods : Atmospheric parameters and abundances were derived in model atmosphere analyses using medium-resolution GIRAFFE or high-resolution UVES ( Ultraviolet and Visual Echelle Spectrograph ) spectra .
These results are part of the fifth internal data release of the Gaia -ESO Survey .
The Li abundances were corrected for non-local thermodynamical equilibrium effects .
Other stellar properties were investigated for additional peculiarities ( the core of strong lines for signs of magnetic activity , infrared magnitudes , rotational velocities , chemical abundances , and Galactic velocities ) .
We used Gaia DR2 parallaxes to estimate distances and luminosities .

Results : The giants have A ( Li ) > 2.2 dex .
The majority of them ( 14 of 20 stars ) are in the CoRoT fields .
Four giants are located in the field of three open clusters , but are not members .
Two giants were observed in fields towards the Galactic bulge , but likely lie in the inner disc .
One of the bulge field giants is super Li-rich with A ( Li ) = 4.0 dex .

Conclusions : We identified one giant with infrared excess at 22 \mu m. Two other giants , with large v~ { } \sin~ { } i , might be Li-rich because of planet engulfment .
Another giant is found to be barium enhanced and thus could have accreted material from a former asymptotic giant branch companion .
Otherwise , in addition to the Li enrichment , the evolutionary stages are the only other connection between these new Li-rich giants .
The CoRoT data confirm that one Li-rich giant is at the core-He burning stage .
The other giants are concentrated in close proximity to the red giant branch luminosity bump , the core-He burning stages , or the early-asymptotic giant branch .
This is very clear from the Gaia -based luminosities of the Li-rich giants .
This is also seen when the CoRoT Li-rich giants are compared to a larger sample of 2252 giants observed in the CoRoT fields by the Gaia -ESO Survey , which are distributed throughout the red giant branch in the T _ { eff } - \log~ { } g diagram .
These observations show that the evolutionary stage is a major factor for the Li enrichment in giants .
Other processes , such as planet accretion , contribute at a smaller scale .