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Originally Posted by Robert Goodman
No, I'm just assuming they're up in the same air, and that there's nothing "funny" (insulating) about the ground between them.
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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.