  We investigate the strongly lensed (\mu x10-100) Lyman continuum (LyC)
galaxy, dubbed Sunburst, at z=2.37, taking advantage of a new accurate model of
the lens. A characterization of the intrinsic (delensed) properties of the
galaxy yields a size of ~3 sq.kpc, a luminosity Muv=-20.3,and a stellar mass
M~10^9 Msun;16% of the ultraviolet light is located in a 3 Myr old
gravitationally-bound young massive star cluster (YMC) with an effective radius
of Re~8 pc and a dynamical mass of ~10^7 Msun (similar to the stellar mass),
from which LyC radiation is detected (\lambda < 912A). The inferred outflowing
gas velocity (>300 km/s) exceeds the escape velocity of the star cluster. The
resulting escape fraction of the ionizing radiation emerging from the Sunburst
galaxy is >6-12%, whilst it is >46-93% if inferred from the YMC. 12 additional
likely star clusters with 3<Re<20 pc are identified in the galaxy from which we
derive a cluster formation efficiency \Gamma>~30%, which is consistent with the
high \Gamma derived in local galaxies experiencing extreme gas physical
conditions. The presence of the YMC influences the morphology (nucleation),
photometry (photometric jumps) and spectroscopic output (nebular emission) of
the entire galaxy. The de-lensed LyC and UV (1600A) magnitudes of the YMC are
~30.6 and ~26.9, whilst the galaxy has m1600~24.8. A relatively large
rest-frame equivalent width of EWrest(Hb+[OIII]4959-5007)~450A emerges from the
galaxy with the YMC contributing to ~30%. If O-type stars are mainly forged in
star clusters, then such engines were the key ionizing agents during
reionization and the increasing occurrence of high EW lines (Hb+[OIII])
observed at z>6.5 might be an indirect signature of a high \Gamma at
reionization.Future facilities (like VLT/MAVIS or ELT), will probe bound
clusters on moderately magnified (\mu<5-10) galaxies across cosmic epochs up to
reionization[ABRIDGED]
