We present an analysis of JWST Lyα spectroscopy of z ≳ 6.5 galaxies, using observations in the public archive covering galaxies in four independent fields: Great Observatories Origins Deep Survey (GOODS)-N, GOODS-S, A2744, and the Extended Groth Strip (EGS). We measure the Lyα emission line properties for a sample of 210 z ≃ 6.5–13 galaxies, with redshifts confirmed independently of Lyα in all cases. We present three new detections of Lyα emission in JWST spectra, including a large equivalent width (EW; =143 Å) Lyα emitter (LAE) with strong C iv emission (EW = 21 Å) at z = 7.1 in GOODS-N. We measure the redshift-dependent Lyα EW distribution across our sample. We find that strong Lyα emission (EW > 25 Å) becomes increasingly rare at earlier epochs, suggesting that the transmission of Lyα photons decreases by 4× between z ≃ 5 and z ≃ 9. We describe potential implications for the intergalactic medium neutral fraction. There is significant field-to-field variance in the LAE fraction. In contrast to the three other fields, the EGS shows no evidence for reduced transmission of Lyα photons at z ≃ 7–8, suggesting a significantly ionized sight line may be present in the field. We use available NIRCam grism observations from the First Reionization Epoch Spectroscopically Complete Observations survey to characterize overdensities on large scales around known LAEs in the GOODS fields. The strongest overdensities appear linked with extremely strong Lyα detections (EW > 50 Å) in most cases. Future Lyα spectroscopy with JWST has the potential to constrain the size of ionized regions around early galaxy overdensities, providing a new probe of the reionization process.