  We consider self-consistent coupling of the recently introduced new class of
Weyl-conformally invariant lightlike branes (WILL-branes) to D=4
Einstein-Maxwell system plus a D=4 three-index antisymmetric tensor gauge
field. We find static spherically-symmetric solutions where the space-time
consists of two regions with different black-hole-type geometries and different
values for a dynamically generated cosmological constant, separated by the
WILL-brane which ``straddles'' their common event horizon. Furthermore, the
WILL-brane produces a potential ``well'' around itself acting as a trap for
test particles falling towards the horizon.
