ABSTRACT We use AStroLens, a newly developed gravitational lens-modelling code that relies only on geometric and photometric information of cluster galaxies as input, to map the strong-lensing regions and estimate the lensing strength of 96 galaxy clusters at z = 0.5–0.9. All clusters were identified during the extended Massive Cluster Survey (eMACS) based on their X-ray flux and optical appearance. Building on the well-tested assumption that the distribution of both luminous and dark matter in galaxy clusters is approximately traced by the distribution of light, i.e. that light traces mass, AStroLens uses three global parameters to automatically model the deflection from strong-gravitational lensing for all galaxy clusters in this diverse sample. We test the robustness of our code by comparing AStroLens estimates derived solely from shallow optical images in two passbands with the results of in-depth lens-modelling efforts for two well-studied eMACS clusters and find good agreement, both with respect to the size and the shape of the strong-lensing regime delineated by the respective critical lines. Our study finds 31 eMACS clusters with effective Einstein radii (θE) in excess of 20″ and eight with θE > 30″, thereby underlining the value of X-ray selection for the discovery of powerful cluster lenses that complement giants like MACSJ0717 at ever-increasing redshift. As a first installment towards the public release of the eMACS sample, we list physical properties of the 10 calibration clusters as well as of the 10 most powerful eMACS cluster lenses, according to AStroLens.