I have read reports that people riding in cars have been severely injured when the cars were struck by lightning. A car would seem to be a fairly good Faraday cage. And it is connected to ground by the carbon black in the tires.
Also, in theory, if the Faraday cage were perfectly spherical, then the electric field inside it would be zero, because all the field vectors from the charges on the surface would cancel each other.
However, if it were not spherical, then the cancellation would not occur, and it would seem that a giant field could be present.
That field could break down the air, and allow a current to flow through the air, and through you if you were near it.
In addition, it seems significant that the lightning may not be like a current in a wire, in the sense that, in the wire, in any imaginary boundary box, the net charge is zero, because the number of protons balances the number of electrons.
However, lightning represents a net movement of charge from the ground to the sky (or the reverse), I believe. Thus, it would seem that the Faraday cage will acquire a net charge, and a gigantic charge at that. I am not sure that a simple analysis is sufficient.
Just a comment.