The ionizing photon escape fraction (LyC fesc) of star-forming galaxies is the single greatest unknown in the reionization budget. Stochastic sightline effects prohibit the direct separation of LyC leakers from non-leakers at significant redshifts. Here we circumvent this uncertainty by inferring fesc using resolved (R > 4000) Lyα profiles from the X-SHOOTER Lyα survey at z = 2 (XLS-z2). With empirically motivated criteria, we use Lyα profiles to select leakers (fesc$>20\%$) and non-leakers (fesc$<5\%$) from a representative sample of >0.2L* Lyman-α emitters (LAEs). We use median stacked spectra of these subsets over λrest ≈ 1000 − 8000Å to investigate the conditions for LyC fesc. Our stacks show similar mass, metallicity, MUV, and βUV. We find the following differences between leakers vs. non-leakers: (i) strong nebular CIV and HeII emission vs. non-detections, (ii) [O iii]/[O ii]≈8.5 vs. ≈3, (iii) Hα/Hβ indicating no dust vs. E(B − V) ≈ 0.3, (iv) MgII emission close to the systemic velocity vs. redshifted, optically thick MgII, (v) Lyα fesc of $\approx 50\%$ vs. $\approx 10\%$. The extreme EWs in leakers ([O iii]+Hβ ≈ 1100 Å rest-frame) constrain the characteristic timescale of LyC escape to ≈3 − 10 Myr bursts when short-lived stars with the hardest ionizing spectra shine. The defining traits of leakers – extremely ionizing stellar populations, low column densities, a dust-free, high ionization state ISM – occur simultaneously in the fesc$>20\%$ stack, suggesting they are causally connected, and motivating why indicators like [O iii]/[O ii] may suffice to constrain fesc at z > 6 with JWST. The leakers comprise half our sample, have a median LyC fesc$\approx 50\%$ (conservative range: $20-55\%$), and an ionising production efficiency $\log ({\xi _{\rm {ion}}/\rm {Hz\ erg^{-1}}})\approx 25.9$ (conservative range: 25.7 − 25.9). These results show LAEs – the type of galaxies rare at z ≈ 2, but that become the norm at higher redshift – are highly efficient ionizers, with extreme ξion and prolific fesc occurring in sync.