Left: Toomre diagram of the new Li-rich giants with good Gaia DR2 parallaxes (i.e. only the 14 giants with a relative error of the parallax lower than 15%). Error bars are shown, but in many cases they are smaller than the point size. Right: chemical plot of the [α/Fe] ratio as a function of [Fe/H]. In all plots, the field Li-rich giants are displayed as stars and giants in fields of open clusters as solid circles. The colour is orange or blue for stars that are tentatively associated with the thick or thin disc, respectively. Other Gaia-ESO iDR5 field stars are shown as dots in the right panel.