In this paper, we study the fundamental limits of simultaneous lightwave information and power transfer (SLIPT) systems over channels with path loss and lognormal fading conditions. We consider a system with a single transmitter transferring information to a photodiode-based receiver as well as transferring energy to a photovoltaic cell receiver. In particular, we study the information-energy capacity region and the optimal input distribution under (a) peak-power and average-power constraints at the transmitter, and (b) the minimum harvest energy at the energy harvesting receiver. To this end, an expression for the transition probability distribution function of the lognormal channel is derived. By extending Smith's framework and using Hermite polynomial bases, we prove that the optimal input distribution is discrete with a finite number of mass points. Information-energy capacity region for SLIPT over lognormal channel conditions is illustrated and compared with the case of additive white Gaussian noise channel.