We propose an indoor lightwave downlink wireless communication network with non-orthogonal multiple access (NOMA), consisting of one visible light communication (VLC) access point (AP) and a pair of randomly located users. Although both users can directly receive information from the AP, the performance of the far user is degraded compared to the near one, due to the asymmetrical channel gains. Thus, we propose user cooperation to improve the performance of the far user, by using mixed VLC/RF relaying in parallel with the wireless optical direct link. In order to efficiently exploit the advantage of this hybrid system, the concept of cross-band selection combining (CBSC) is introduced, while its performance is thoroughly investigated and compared to appropriate baselines, according to which the far user is continuously served by either the mixed VLC/RF or the direct VLC link. To this end, we derive closed-form expressions for the outage probability of each user as well as the system sum throughput. Finally, simulation results are provided to verify the effectiveness of the proposed scheme and the accuracy of the corresponding analysis. Index Terms-Lightwave, hybrid system, decode-and-forward relaying, non-orthogonal multiple access (NOMA), cross band selection combining (CBSC).