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It would crash.

A dirigible requires a temperature difference between the ambient (surrounding) air and the air inside the lift bladder. Or the same temperature but different density.

The heat of the lava would create an area of lower air density which would result in a significant loss of lift as it crosses.

I guess you could compensate with a high altitude crossing, but it still sounds dangerous.

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This situation was covered in season 3 of Avatar The Last Airbender, and that is exactly what happened. Such a great show.

It really was. But it's possible the volcanic lake only projected a captured cell of hot air up to the crater rim. Had they flown over the prison and then directly down they might not have crashed. Though they would still be trapped.

If only Zuko had his fire fists or that of his sister Azula at that point it would have been easier.

Man Uncle Iroh is OP with the fire breath technique he teaches Zuko for the "chillers"

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