We present a strong-lensing analysis of the cluster PSZ1 G311.65−18.48, based on Hubble Space Telescope imaging, archival VLT/MUSE spectroscopy, and Chandra X-ray data. This cool-core cluster (z = 0.443) lenses the brightest lensed galaxy known, dubbed the “Sunburst Arc” (z = 2.3703), a Lyman continuum (LyC) emitting galaxy multiply imaged 12 times. We identify in this field 14 additional strongly lensed galaxies to constrain a strong-lens model and report secure spectroscopic redshifts of four of them. We measure a projected cluster core mass of M(<250 kpc) =
2.93
−
0.02
+
0.01
×
10
14
M
⊙. The two least magnified but complete images of the Sunburst Arc’s source galaxy are magnified by ∼13×, while the LyC clump is magnified by ∼4–80×. We present time delay predictions and conclusive evidence that a discrepant clump in the Sunburst Arc, previously claimed to be a transient, is not variable, thus strengthening the hypothesis that it results from an exceptionally high magnification. A source plane reconstruction and analysis of the Sunburst Arc finds its physical size to be 1 × 2 kpc and that it is resolved in three distinct directions in the source plane, 0°, 40°, and 75° (east of north). We place an upper limit of r ≲ 50 pc on the source plane size of unresolved clumps and r ≲ 32 pc for the LyC clump. Finally, we report that the Sunburst Arc is likely in a system of two or more galaxies separated by ≲6 kpc in projection. Their interaction may drive star formation and could play a role in the mechanism responsible for the leaking LyC radiation.