This study presents a lightning-inspired method of fundamental solutions for the numerical solution of two-dimensional Laplace equations with discontinuous boundary data. The proposed approach combines the classical method of fundamental solutions, a boundary-type meshless technique that satisfies the governing Laplace equation exactly, with ideas motivated by lightning methods, which employ clustered source locations to achieve rapid convergence and high accuracy. In the solution procedure, fundamental solution sources are placed regularly outside the computational domain and arranged using lightning-type geometrical clustering near boundary discontinuities, corners, and regions of rapid solution variation. This source distribution significantly enhances the approximation capability compared with conventional placement strategies in the method of fundamental solutions. The resulting scheme is simple to implement, computationally efficient, and capable of resolving discontinuous boundary features accurately. This study shows that lightning-inspired source placement provides an effective and powerful framework for solving Laplace equations with challenging boundary data.