This paper investigates a downlink power allocation scheme for application of non-orthogonal multiple access (NOMA) in visible light communication (VLC) systems. Aiming to achieve a flexible tradeoff between sum rate and user fairness depending on administrators' subjective setting and acquire the optimal solution for any setting, we formulate two optimization problems, which are closely aligned with the practical application. Specifically, one is user fairness-guaranteed sum rate maximization, the other is sum rate-guaranteed user fairness maximization. Moreover, through classified discussion around the threshold guaranteeing user fairness or sum rate, we present rigorous mathematical derivation and optimization analysis, and two corresponding algorithms are proposed. Furthermore, through numerical simulation, the superiority of our proposed algorithms over conventional schemes is verified in terms of meeting the practical demand and performance gain in sum rate, user fairness, and coverage probability.