In this paper, we study the secrecy performance of non-orthogonal multiple access (NOMA) enabled visible light communication (VLC) broadcast channels in the presence of an active eavesdropper (Eve). The considered VLC system consists of multiple separately distributed light-emitting diodes arrays and multiple randomly located users (UEs) in an indoor room. User clustering is conducted to reduce the implementation complexity of successive interference cancellations. Two cooperative precoding strategies based on zero-forcing (ZF) and maximum ratio transmission (MRT) are designed using the effective channel of each cluster. Based on each precoding strategy, a sum secrecy rate maximization problem is developed to obtain the near-optimal power allocation (PA) to strengthen UEs’ confidential transmission and degrade Eve’s reception under minimum secrecy rate requirement, peak amplitude, non-negativity, and power constraints. To tackle the challenging non-convex problem for each precoding strategy, equivalent transformations and arithmetic-geometric mean approximation are conducted to convert the original problem into a series of geometric programming (GP) problems. Based on the reformulated problems, iterative algorithms are proposed to obtain near-optimal solutions by solving the GP problems through successive convex approximations. The convergence and complexity analysis of the proposed algorithms are studied. Simulation results show that the sum security performance of the proposed PA approach outperforms the conventional PA approaches in both ZF-based and MRT-based precoder schemes. The effectiveness of applying NOMA compared with the orthogonal multiple access-based scheme is also validated for the proposed system.