The chromospheric Lyman‐alpha line of neutral hydrogen (Lyα; 1216 Å) is the strongest emission line in the solar spectrum. Fluctuations in Lyα are known to drive changes in planetary atmospheres, although few instruments have had the ability to capture rapid Lyα enhancements during solar flares. In this paper, we describe flare‐associated emissions via a statistical study of 477 M‐ and X‐class flares as observed by the Extreme UltraViolet Sensor on board the 15th Geostationary Operational Environmental Satellite, which has been monitoring the full‐disk solar Lyα irradiance on 10‐s timescales over the course of Solar Cycle 24. The vast majority (95%) of these flares produced Lyα enhancements of 10% or less above background levels, with a maximum increase of ∼30%. The irradiance in Lyα was found to exceed that of the 1–8 Å X‐ray irradiance by as much as two orders of magnitude in some cases, although flares that occurred closer to the solar limb were found to exhibit less of a Lyα enhancement. This center‐to‐limb variation was verified through a joint, stereoscopic observation of an X‐class flare that appeared near the limb as viewed from Earth, but close to disk center as viewed by the MAVEN spacecraft in orbit around Mars. The frequency distribution of peak Lyα was found to have a power‐law slope of 2.8±0.27. We also show that increased Lyα flux is closely correlated with induced currents in the ionospheric E‐layer through the detection of the solar flare effect as observed by the Kakioka magnetometer.