We investigate the gas-phase metallicity and Lyman Continuum (LyC) escape fraction of a strongly gravitationally lensed, extreme emission-line galaxy at z = 3.417, J1000 + 0221S, recently discovered by the CANDELS team. We derive ionization and metallicity sensitive emission-line ratios from H+K band LBT/LUCI medium resolution spectroscopy. J1000 + 0221S shows high ionization conditions, as evidenced by its enhanced [O iii]/[O ii] and [O iii]/Hβ ratios. Consistently, strong-line methods based on the available line ratios suggest that J1000 + 0221S is an extremely metal-poor galaxy, with a metallicity of 12+ log(O/H)<7.44 (Z < 0.05 Z ⊙ , placing it among the most metal-poor star-forming galaxies at z 3 discovered so far. In combination with its low stellar mass (2×10 8 M ⊙ ) and high star formation rate (5 M ⊙ yr −1 ), the metallicity of J1000 + 0221S is consistent with the extrapolation to low masses of the mass-metallicity relation traced by Lyman-break galaxies at z 3, but it is 0.55 dex lower than predicted by the fundamental metallicity relation at z 2.5. These observations suggest the picture of a rapidly growing galaxy, possibly fed by the massive accretion of pristine gas. Additionally, deep LBT/LBC in the UGR bands are used to derive a limit to the LyC escape fraction, thus allowing us to explore for the first time the regime of sub-L * galaxies at z > 3. We find a 1σ upper limit to the escape fraction of 23%, which adds a new observational constraint to recent theoretical models predicting that sub-L * galaxies at high-z have high escape fractions and thus are the responsible for the reioization of the Universe.