Context. Previous studies of open clusters have shown that lithium depletion is not only strongly age dependent but also shows a complex pattern with other parameters that is not yet understood. For pre- and main-sequence late-type stars, these parameters include metallicity, mixing mechanisms, convection structure, rotation, and magnetic activity. Aims. We perform a thorough membership analysis for a large number of stars observed within the Gaia-ESO survey (GES) in the field of 20 open clusters, ranging in age from young clusters and associations, to intermediate-age and old open clusters. Methods. Based on the parameters derived from the GES spectroscopic observations, we obtained lists of candidate members for each of the clusters in the sample by deriving radial velocity distributions and studying the position of the kinematic selections in the EW(Li)-versus-T_eff plane to obtain lithium members. We used gravity indicators to discard field contaminants and studied [Fe/H] metallicity to further confirm the membership of the candidates. We also made use of studies using recent data from the Gaia DR1 and DR2 releases to assess our member selections. Results. We identified likely member candidates for the sample of 20 clusters observed in GES (iDR4) with UVES and GIRAFFE, and conducted a comparative study that allowed us to characterize the properties of these members as well as identify field contaminant stars, both lithium-rich giants and non-giant outliers. Conclusions. This work is the first step towards the calibration of the lithium–age relation and its dependence on other GES parameters. During this project we aim to use this relation to infer the ages of GES field stars, and identify their potential membership to young associations and stellar kinematic groups of different ages.