We present a modification of a model of solar cycle evolution of the solar Lyman-alpha line profile, along with a sensitivity study of interstellar neutral H hydrogen to uncertainties in radiation pressure level. The line profile model, originally developed by Kowalska-Leszczynska et al. 2018a, is parametrized by the composite solar Lyman-alpha flux, which recently was revised Machol et al. 2019. We present modified parameters of the previously-developed model of solar radiation pressure for neutral hydrogen and deuterium atoms in the heliosphere. The mathematical function used in the model, as well as the fitting procedure, remain unchanged. We show selected effects of the model modification on ISN H properties in the heliosphere and we discuss the sensitivity of these quantities to uncertainties in the calibration of the composite Lyman-alpha series.