The H I Lyman-alpha emission at 121.6 nm is a dominant emission in the far ultraviolet (FUV) solar spectrum. This emission is primarily from the chromosphere and transition region, and it varies by about a factor of 2 over the solar cycle. The Lyman-alpha irradiance has been measured for over 30 years, and a time composite of these measurements has been compiled for long-term studies of the solar variability. The measurements and models of the solar Lyman-alpha irradiance permit an examination of the possible changes of the solar UV irradiance during the Maunder Minimum period in the 1600s. There are two known components that can reduce the solar irradiance below the current solar cycle minimum irradiance levels. For one, the active network area on the solar disk is not zero during solar minimum. Secondly from SOHO SUMER measurements, the quiet Sun radiance changes with solar cycle activity with lower quiet Sun radiance during solar cycle minimum. Accounting for these effects, the estimated change of the Lyman-alpha irradiance during the Maunder Minimum is a 25% decrease relative to the current solar cycle minimum conditions.