We demonstrate how the stellar and nebular conditions in star-forming galaxies modulate the emission and spectral profile of H I Ly α emission line. We examine the net Ly α output, kinematics, and in particular emission of blueshifted Ly α radiation, using spectroscopy from with the Cosmic Origins Spectrograph on Hubble Space Telescope (HST), giving a sample of 87 galaxies at redshift z = 0.05−0.44. We contrast the Ly α spectral measurements with properties of the ionized gas (from optical spectra) and stars (from stellar modelling). We demonstrate correlations of unprecedented strength between the Ly α escape fraction (and equivalent width) and the ionization parameter (p ≈ 10⁻¹⁵). The relative contribution of blueshifted emission to the total Ly α also increases from ≈0 to ≈40 per cent over the range of O₃₂ ratios (p ≈ 10⁻⁶). We also find particularly strong correlations with estimators of stellar age and nebular abundance, and weaker correlations regarding thermodynamic variables. Low ionization stage absorption lines suggest the Ly α emission and line profile are predominantly governed by the column of absorbing gas near zero velocity. Simultaneous multiparametric analysis over many variables shows we can predict 80 per cent of the variance on Ly α luminosity, and ∼50 per cent on the EW. We determine the most crucial predictive variables, finding that for tracers of the ionization state and H β luminosity dominate the luminosity prediction whereas the Ly α EW is best predicted by H β EW and the H α/H β ratio. We discuss our results with reference to high-redshift observations, focussing upon the use of Ly α to probe the nebular conditions in high-z galaxies and cosmic reionization.