The cosmic ionizing emissivity from star-forming galaxies has long been anchored to UV luminosity functions. Here, we introduce an emissivity framework based on Lyα emitters (LAEs), which naturally hones in on the subset of galaxies responsible for the ionizing background due to the intimate connection between production and escape of Lyα and LyC photons. Using constraints on the escape fractions of bright LAEs (LLyα > 0.2L*) at z ≍ 2 obtained from resolved Lyα profiles, and arguing for their redshift-invariance, we show that: (i) quasars and LAEs together reproduce the relatively flat emissivity at z ≍ 2-6, which is non-trivial given the strong evolution in both the star formation density and quasar number density at these epochs and (ii) LAEs produce late and rapid reionization between z ≍ 6-9 under plausible assumptions. Within this framework, the >10 × rise in the UV population-averaged fesc between z ≍ 3-7 naturally arises due to the same phenomena that drive the growing LAE fraction with redshift. Generally, a LAE dominated emissivity yields a peak in the distribution of the ionizing budget with UV luminosity as reported in latest simulations. Using our adopted parameters ($f_{\rm {esc}}=50{{\ \rm per\ cent}}$, ξion = 1025.9 Hz erg-1 for half the bright LAEs), a highly ionizing minority of galaxies with MUV < -17 accounts for the entire ionizing budget from star-forming galaxies. Rapid flashes of LyC from such rare galaxies produce a 'disco' ionizing background. We conclude proposing tests to further develop our suggested Lyα-anchored formalism.