Robert Goodman wroteNo, I'm just assuming they're up in the same air, and that there's nothing "funny" (insulating) about the ground between them.
That's my point. The ground is the insulation and the conductor. An insulator is nothing more than high resistance. Get the potential (i.e. voltage) high enough, and all insulators become conductors. Thus during a lightning strike, the ground becomes that conductor.
In order for it to function as a Faraday cage, i.e. to eliminate the possibility of any electrical field being present within the ring, they would have to be electrically connected with a low resistance path. The ground would be the electrical connection, thus would be the path for any discharge. Anybody between the towers would be at risk. A lower resistance path, such as heavy gauge wires between the towers, would protect against these currents.