Given that the clues of the lottery seem to point toward the panserbjorne of Svalbard, I will tell you what I know of them.
The two riddles seemed to imply "ice" and "bear". The map was fairly self-explanatory; it had Svalbard circled. I'm not certain what the alethiometer is meant to represent in the theme present. The bears don't use them. The prophecy child, Lyra, had one, and she did trick the bear-king into agreeing to engage in single combat with a challenger. Perhaps we're meant to trick the bears, but I won't speculate on that.
Alethiometer are used to detect the truth in things. The explanation is lengthy and I believe pointless in context, but perhaps someone else may be able to work out the relevance of one in the theme of clues. I'd be willing to go into what I know of them if anyone believes it would be helpful.
The panserbjorne are generally solitary creatures, though their kingdom is in the far north, centered near Svalbard. They have a monarchy, though the king can be displaced by losing a challenge of single combat to another bear. The bear king when I was taken was Iorek Byrnison, who was a friend to the prophecy child. There may be some connection there, but again, I won't offer any speculation.
The bears are known as armor-bears because of their skills as metal smiths and their ability to form intricate armor from a substance they call 'sky-iron', or metal obtained from meteorites. Their armor is to them what dæmon are to us. They pour themselves into their armor; it is their protection from other bears and it may bear some symbolism, but any other superstition attached to the armor remains a secret from me.
It did once reach my ear that Iorek's armor was stolen from him and the men who took it did not live to tell of it, but that is third or fourth hand knowledge and I don't know how reliable it is.
I don't know if any of this is helpful, and I'd be willing to expand upon any points anyone thinks may be relevant.
- Isadora