It's a good place to be, but lightning is a bit unpredictable. The cage needs to be grounded. If the ground path passes under your feet, you could get a voltage differential across the two of them, causing severe harm to you.
Your feet should be on a dry, elevated wood platform. If the wood gets wet from rain coming through, there is again the possibility of a voltage differential.
The cage would be electrically equivalent to a Faraday cage, and therefore safe, it it was metal on six sides, joined together through low resistance, reliable bonds.