This letter studies rate-splitting multiple access (RSMA)-based visible light communication (VLC) network employing simultaneous light-wave information and power transfer (SLIPT) technology to assist multiple Internet of Things (IoT) devices while achieving self-sustainability. We formulate a fairness problem to maximize the minimum harvested energy among IoT devices to maximize network longevity by jointly optimizing the precoding matrix and direct current bias vector, subject to information flow control and total transmit power. An iterative approach is proposed to obtain a sub-optimal solution. Simulation results reveal the superiority of the proposed RSMA-based network over existing schemes under different network load scenarios, including underloaded and overloaded conditions.