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I wonder if anyone has tried feeding a skyscraper's lighting rod into a sand battery and let it charge up from lightning alone, so much potential for free energy there.

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It would never strike the lightning rod. The entire reason lightning strikes is due to a circuit between the clouds and ground. If you were to put a "battery" like this somewhere, then the resistance would cause the lightning to go where you don't want it.

I am aware of no energy storage system capable of absorbing 250000 Wh in under a second

You just need to use a sufficiently large storage system. One of the proposals of Project Plowshare was to use underground detonation of thermonuclear weapons as a geothermal energy sources.

There is a huge difference between electrical energy trying to find its way to ground the easiest way possible (lightning), and a nuke.

For one, lighting can almost certainly find an easier path than into the battery.

For a nuke, the easiest path (once triggered) is to explode.

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