  We propose a general action describing the dynamics of lightlike (LL)
p-branes in any odd (p+1) world-volume dimensions. Next, we consider
self-consistent coupling of \textsl{LL}-membranes (p=2) to D=4 Einstein-Maxwell
system plus a D=4 three-index antisymmetric tensor gauge field. The LL-brane
serves as a material and charge source for gravity and electromagnetism and,
furthermore, it produces a dynamical space-varying cosmological constant. We
present static spherically-symmetric solutions where the space-time consists of
two regions with different black-hole-type geometries and different values for
dynamically generated cosmological constant, separated by the LL-brane which
"straddles" their common event horizon.
