The ionizing photon escape fraction [Lyman continuum (LyC) f(esc)] 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 f(esc) using resolved (R > 4000) Lyman alpha (Ly alpha) profiles from the X-SHOOTER Ly alpha survey at z = 2 (XLS-z2). With empirically motivated criteria, we use Ly alpha profiles to select leakers (f(esc) > 20 per cent) and non-leakers (f(esc) < 5 per cent) from a representative sample of >0.2L* Lyman alpha emitters (LAEs). We use median stacked spectra of these subsets over lambda(rest) approximate to 1000-8000 angstrom to investigate the conditions for LyC f(esc). Our stacks show similar mass, metallicity, M-UV, and beta(UV). We find the following differences between leakers versus non-leakers: (i) strong nebular C IV and He II emission versus non-detections; (ii) [O III]/[O II] approximate to 8.5 versus approximate to 3; (iii) H alpha/H beta indicating no dust versus E(B - V) approximate to 0.3; (iv) Mg II emission close to the systemic velocity versus redshifted, optically thick Mg II; and (v) Ly alpha f(esc) of approximate to 50 per cent versus approximate to 10 per cent. The extreme equivalent widths (EWs) in leakers ([O III]+H beta approximate to 1100 Arest frame) constrain the characteristic time-scale of LyC escape to approximate 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 interstellar medium (ISM) - occur simultaneously in the f(esc) > 20 per cent stack, suggesting they are causally connected, and motivating why indicators like [O III]/[O II] may suffice to constrain f(esc) at z > 6 with the James Webb Space Telescope (JWST). The leakers comprise half of our sample, have a median LyC f(esc) approximate to 50 per cent (conservative range: 20-55 per cent), and an ionizing production efficiency log(xi(ion)/Hz erg(-1)) approximate to 25.9 (conservative range: 25.7-25.9). These results show LAEs - the type of galaxies rare at z approximate to 2, but that become the norm at higher redshift - are highly efficient ionizers, with extreme xi(ion) and prolific f(esc) occurring in sync.