- We consider a self‐consistent Einstein‐Maxwell‐Kalb‐Ramond system in the bulk D = 4 space‐time interacting with a variable‐tension electrically charged lightlike brane . The latter serves both as a material and charge source for gravity and electromagnetism, as well as it dynamically generates a bulk space varying cosmological constant. We find an asymmetric wormhole solution describing two “universes” with different spherically symmetric black‐hole‐type geometries connected through a “throat” occupied by the lightlike brane. The electrically neutral “left universe” comprises the exterior region of Schwarzschild‐de‐Sitter (or pure Schwarzschild) space‐time above the inner (Schwarzschild‐type) horizon, whereas the electrically charged “right universe” consists of the exterior Reissner‐Nordström (or Reissner‐Nordström‐de‐Sitter) black hole region beyond the outer Reissner‐Nordström horizon. All physical parameters of the wormhole are uniquely determined by two free parameters—the electric charge and Kalb‐Ramond coupling of the lightlike brane.