We analyze the light curves of the recent solar eclipses measured by the Herzberg channel (200-220 nm) of the Large Yield RAdiometer (LYRA) onboard PROBA-2. The measurements allow us to accurately retrieve the center- to-limb variations (CLV) of the solar brightness. The formation height of the radiation depends on the observing angle so the examination of the CLV provide information about a broad range of heights in the solar atmosphere. We employ the 1D NLTE radiative transfer COde for Solar Irradiance (COSI) to model the measured light curves and corresponding CLV dependencies. The modeling is used to test and constrain the existing 1D models of the solar atmosphere, e.g. the temperature structure of the photosphere and the treatment of the pseudo- continuum opacities in the Herzberg continuum range. We show that COSI can accurately reproduce not only the irradiance from the entire solar disk, but also the measured CLV. It hence can be used as a reliable tool for modeling the variability of the spectral solar irradiance.