Lognormal channel is a powerful mathematical tool in modeling fading effects for wireless optical communications over weak turbulence channels. However, exact analysis involving lognormal channels involves multi-fold integrals, which reveal little insights into the relation between the system performance and the channel parameters. Therefore, Wilkinson Approximation (WA) and Fenton Approximation (FA) are widely applied to approximate the performance of lognormal fading channels. However, their ranges of applications are not fully studied, which causes discrepancies in performance evaluations. In this work, we compare WA and FA based on the expressions of moments, and propose an approach to approximate the performance of Free-Space Optical Communications (FSO) relaying systems over the lognormal weak turbulence channels, and discuss the ranges of applications for WA and FA. It is shown that at low and medium Signal-to-Noise Ratio (SNR), error probability approximation based on WA is more accurate. However, at large SNR, Fenton’s approach will provide better approximation accuracy compared to the WA. Simulation results indicate that the approximation error depends on the discrepancies between the variances over FSO links as well as the scintillation level of the channels.