- We study self-consistent D=4 gravity-matter systems coupled to a new class of Weyl-conformally invariant lightlike branes (WILL}-branes). The latter serve as material and charged source for gravity and electromagnetism. Further, due to the natural coupling to a 3-index antisymmetric tensor gauge field, the WILL-brane dynamically produces a space-varying bulk cosmological constant. We find static spherically-symmetric solutions where the space-time consists of two regions with black-hole-type geometries separated by the WILL-brane which "straddles" their common event horizon and, therefore, provides an explicit dynamical realization of the "membrane paradigm" in black hole physics. Finally, by matching via WILL-brane of internal Schwarzschild-de-Sitter with external Reissner-Nordstrom-de-Sitter (or external Schwarzschild-de-Sitter)geometries we discover the emergence of a potential "well" for infalling test particles in the vicinity of the WILL-brane (the common horizon) with a minimum on the brane itself.