We show the effectiveness of strong lensing in the characterization of Lyman continuum emission from faint L≲ 0.1L* star-forming galaxies at redshift ≳3. Past observations of L≳L* galaxies at redshift ≳3 have provided upper limits of the average escape fraction of ionizing radiation of fesc∼ 5 per cent. Galaxies with relatively high fesc (>10 per cent) seem to be particularly rare at these luminosities; there is therefore the need to explore fainter limits. Before the advent of giant ground-based telescopes, one viable way to probe fesc down to 0.05–0.15L* was to exploit strong lensing magnification. This is investigated with Monte Carlo simulations that take into account the current observational capabilities. Adopting a lensing cross-section of 10 arcmin2 within which the magnification is higher than 1 (achievable with about four to five galaxy clusters), with a U-band survey depth of 30 (30.5) (AB, 1σ), it is possible to constrain fesc for z≃ 3 star-forming galaxies down to 15 (10) per cent at 3σ for L < 0.15L* luminosities. This is particularly interesting if fesc increases at fainter luminosities, as predicted from various H i reionization scenarios and radiation transfer modelling. Ongoing observational programmes on galaxy clusters are discussed and positive prospects for the future are offered, even though from space the Hubble Space Telescope (HST)/Wide Field Camera 3 (WFC3) instrument represents the only option we have to investigate details of the spatial distribution of the Lyman continuum emission arising from z∼ 2–4 galaxies.