Lyman-α (Lyα) spectra provide insights into the small-scale structure and kinematics of neutral hydrogen (HI) within galaxies as well as the ionization state of the intergalactic medium (IGM). The former defines the intrinsic spectrum of a galaxy, which, in turn, is modified by the latter. These two effects are degenerate. Using the IllustrisTNG100 simulation, we studied the impact of the IGM on Lyα spectral shapes between z ∼ 0 and 5. We computed the distribution of the expected Lyα peaks and of the peak asymmetry for different intrinsic spectra, redshifts, and large-scale environments. We find that the averaged transmission curves that are commonly applied give a misleading perception of the observed spectral properties. We show that the distributions of peak counts and asymmetry can lift the degeneracy between the intrinsic spectrum and IGM absorption. For example, we expect a significant number of triple-peaked Lyα spectra (up to 30% at z ∼ 3) if the galaxies’ HI distribution become more porous at higher redshift, as predicted by cosmological simulations. We provide a public catalog of transmission curves for simulations and observations to allow for a more realistic IGM treatment in future studies.