What discovery leads Turin and Niniel to take their own lives in Unfinished Tales: The Lost Lore of Middle-earth?

When Turin marries Niniel, he does so having never seen her before (Turin was sent away by his mother when he was small to be raised by elves), so he doesn't know that Niniel is his sister. She, in turn, has no way of knowing that he is her brother; after all, her memory has been wiped clear by the dragon, and she can't even remember her own real name. Ironically, their marriage appears in the beginning to be quite happy, and they are quite in love. It is only after the would-be climax to the story during which Turin kills the dragon that they find out their true relationship. When each finds out, they both end up committing suicide.