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Abstract JWST observations have recently begun delivering the first samples of Lyαvelocity profile measurements atz> 6, opening a new window into the reionization process. Interpretation ofz≳ 6 line profiles is currently stunted by limitations in our knowledge of the intrinsic Lyαprofile (before encountering the intergalactic medium (IGM)) of the galaxies that are common atz≳ 6. To overcome this shortcoming, we have obtained resolved (R∼ 3900) Lyαspectroscopy of 42 galaxies atz= 2.1–3.4 with similar properties as are seen atz> 6. We quantify a variety of Lyαprofile statistics as a function of [Oiii]+Hβequivalent width (EW). Our spectra reveal a new population ofz≃ 2–3 galaxies with large [Oiii]+HβEWs (>1200 Å) and a large fraction of Lyαflux emerging near the systemic redshift (peak velocity ≃0 km s⁻¹). These spectra indicate that low-density neutral hydrogen channels are able to form in a subset of low-mass galaxies (≲1 × 10⁸M_⊙) that experience a burst of star formation (sSFR > 100 Gyr⁻¹). Other extreme [Oiii] emitters show weaker Lyαthat is shifted to higher velocities (≃240 km s⁻¹) with little emission near the line center. We investigate the impact the IGM is likely to have on these intrinsic line profiles in the reionization era, finding that the centrally peaked Lyαemitters should be strongly attenuated atz≳ 5. We show that these line profiles are particularly sensitive to the impact of resonant scattering from infalling IGM and can be strongly attenuated even when the IGM is highly ionized atz≃ 5. We compare these expectations against a new database ofz≳ 6.5 galaxies with robust velocity profiles measured with JWST/NIRSpec.