A conventional approach to tackle the inter-cell interference in multi-cell visible light communication (VLC) networks is based on non-orthogonal multiple access (NOMA) by allowing one user to fully decode the message of another user. Due to the ability of partially decoding the interference and partially treating it as noise, rate-splitting multiple access (RSMA) has been regarded as a more flexible interference management scheme that generalizes and outperforms NOMA. Motivated by the benefits of RSMA and its infancy in multi-cell VLC networks, this paper firstly introduces 1-layer RSMA into multi-cell VLC networks by considering the Lambertian radiation model of indoor visible-light channels. Afterwards, we develop a linear precoding containing 1-layer RSMA-VLC to achieve spectral efficiency having constrained the non-linear effect of a light-emitting diode (LED). Subsequently, the transmitted power allocation is constrained by the optical signal power. Finally, we perform a comparison between 1-layer RSMA and NOMA based on multi-cell VLC networks. Simulation results show the effectiveness of our proposal in system spectral efficiency and VLC constraints. Furthermore, key features guaranteeing the merits of 1-layer RSMA are analysed with respect to the number of users, user locations, and lighting deployment.