The Lyman-alpha (Ly{alpha}) line of neutral hydrogen at 121.6nm is by far the brightest emission line in the vacuum ultraviolet spectral range of the Sun. The emission at this line could be a major energy input to the upper layers of the Earth's atmosphere, strongly impacting the geospace environment. The Geostationary Operational Environmental Satellite (GOES) series, starting with GOES-13, began to carry a multichannel Extreme UltraViolet Sensor (EUVS) with one channel (E-channel) targeting the Ly{alpha} line. In the present work, we produce a Ly{alpha} flare catalog from the GOES-15/EUVS-E data between 2010 April 8 and 2016 June 6 with an automatic flare detection algorithm. This algorithm is designed to search events at various scales and find their real start and end times. Based on the obtained flare list, statistics on the temporal behavior such as the duration, rise, and decay times, and the event asymmetries of Ly{alpha} flares is presented. On average (defined by the median of the distributions), the duration, rise and decay times of the flares were estimated to be 20.8 minutes, 5.6 minutes, and 14.2 minutes, respectively. We also discuss the frequency distributions of the peak flux and the fluence of Ly{alpha} flares, both of which reveal power-law behaviors with power-law indices of 2.71+/-0.06 and 2.42+/-0.06, respectively, implying that more flares are accumulated at small scales and these small-scale events play an important role in explaining the violent solar energy release.