As the Lyman-alpha (Lyα ) line of neutral hydrogen is the brightest emission line in the solar spectrum, detecting increases in irradiance due to solar flares at this wavelength can be challenging due to the very high background. Previous studies that have focused on the largest flares have shown that even these extreme cases generate enhancements in Lyα of only a few percent above the background. In this study, a superposed-epoch analysis was performed on ≈8500 flares greater than B1 class to determine the contribution that they make to changes in the solar EUV irradiance. Using the peak of the 1 - 8 Å X-ray emission as a fiducial time, the corresponding time series of 3123 B- and 4972 C-class flares observed in Lyα emission by the EUV Sensor on the Geostationary Operational Environmental Satellite 15 (GOES-15) were averaged to reduce background fluctuations and improve the flare signal. The summation of these weaker events showed that they produced a 0.1 - 0.3% enhancement to the solar Lyα irradiance on average. For comparison, the same technique was applied to 453 M- and 31 X-class flares, which resulted in a 1 - 4% increase in Lyα emission. Flares were also averaged with respect to their heliographic angle to investigate any potential center-to-limb variation. For each GOES class, the relative enhancement in Lyα at the flare peak was found to diminish for flares that occurred closer to the solar limb due to the opacity of the line and/or foreshortening of the footpoints. One modest event included in the study, a C6.6 flare, exhibited an unusually high increase in Lyα of 7% that may have been attributed to a failed filament eruption. Increases of this magnitude have hitherto only been associated with a small number of X-class flares.