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Context. With its origin coming from several sources (Big Bang, stars, cosmic rays) and given its strong depletion during its stellar lifetime, the lithium element is of great interest as its chemical evolution in the Milky Way is not well understood at present. To help constrain stellar and galactic chemical evolution models, numerous and precise lithium abundances are necessary for a large range of evolutionary stages, metallicities, and Galactic volume. Aims. In the age of stellar parametrization on industrial scales, spectroscopic surveys such as APOGEE, GALAH, RAVE, and LAMOST have used data-driven methods to rapidly and precisely infer stellar labels (atmospheric parameters and abundances). To prepare the ground for future spectroscopic surveys such as 4MOST and WEAVE, we aim to apply machine learning techniques to lithium measurements and analyses. Methods. We trained a convolution neural network (CNN), coupling Gaia-ESO Survey iDR6 stellar labels (Teff, log(g), [Fe/H], and A(Li)) and GIRAFFE HR15N spectra, to infer the atmospheric parameters and lithium abundances for ∼40 000 stars. The CNN architecture and accompanying notebooks are available online via GitHub. Results. We show that the CNN properly learns the physics of the stellar labels, from relevant spectral features through a broad range of evolutionary stages and stellar parameters. The lithium feature at 6707.8 Å is successfully singled out by our CNN, among the thousands of lines in the GIRAFFE HR15N setup. Rare objects such as lithium-rich giants are found in our sample. This level of performance is achieved thanks to a meticulously built, high-quality, and homogeneous training sample. Conclusions. The CNN approach is very well adapted for the next generations of spectroscopic surveys aimed at studying (among other elements) lithium, such as the 4MIDABLE-LR/HR (4MOST Milky Way disk and bulge low- and high-resolution) surveys. In this context, the caveats of machine-learning applications should be appropriately investigated, along with the realistic label uncertainties and upper limits for abundances. [ABSTRACT FROM AUTHOR]