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This paper proposes and optimizes a cooperative non-orthogonal multiple-access (Co-NOMA) scheme in the context of multicell visible light communications (VLC) networks, as a means to mitigate inter-cell interference in Co-NOMA-enabled systems. Consider a network with multiple VLC access points (APs), where each AP serves two users using light intensity. In each cell, the weak user (the cell edge user) can be served either directly by the VLC AP, or through the strong user that can decode the weak user's message and forward it through the radio-frequency (RF) link. The paper then considers the problem of maximizing the network throughput under quality-of-service (QoS) constraints by allocating the powers of the users' messages and APs' transmit powers, and determining the serving links of each weak user (i.e., VLC or hybrid VLC/RF). The paper solves such a non-convex problem by first finding closed form solutions of the joint users' powers and link selection for a fixed AP power allocation. The APs' transmit powers are then iteratively solved in an outer loop using the golden section method. Simulation results show how the proposed solution and scheme improve the system sum-rate and fairness as compared to conventional non-orthogonal multiple-access (NOMA) schemes.