Visible light communication (VLC) has emerged as one promising candidate technique to improve the throughput performance in future sixth-generation (6G) mobile communication networks. Due to the limited battery capacity of VLC systems, light energy harvesting has been proposed and incorporated for achieving the simultaneous lightwave information and power transfer (SLIPT) function and for improving the overall energy efficiency. Nevertheless, almost all reported works are limited to SLIPT scenarios adopting a basic and well-discussed Lambertian optical transmitter, which definitely cannot characterize the potential and essential scenarios employing distinctive non-Lambertian optical transmitters with various spatial beam characteristics. For addressing this issue, in this work, SLIPT based on a distinct non-Lambertian optical beam configuration is investigated, and for further enhancing the harvested energy and the achievable data rate, the relevant flexible optical beam configuration method is presented as well. The numerical results show that, for a typical receiver position, compared with about 1.14 mJ harvested energy and a 31.2 Mbps achievable data rate of the baseline Lambertian configuration, a harvested energy gain of up to 1.55 mJ and an achievable data rate gain of 21.1 Mbps can be achieved by the non-Lambertian SLIPT scheme explored here.