A lightning strike protection system for protecting composite structures, an improved lightning strike appliqué (LSA) for such a lightning strike protection system, and a method of protecting composite structures, such as an aircraft fuselage. The LSA is electrically connected to adjacent conductive surfaces, e.g., by a fuzz button or a wire bond inserted in the bottom of the LSA. An adjacent conductive surface may be another LSA, a lightning diverter overlay, or a current return network. Charge, e.g., from a lightning strike to the LSA, flows to the conductive layer through the electrical connector.