The third life—the switch from piggie to tree—is a symbol for going to heaven. It's not especially subtle, and Human even specifically compares turning into a tree to the account of the afterlife in the Bible, saying "But the other book you gave us. It talked all the time about living after death and being born again" (17.357). And Quim, the good Catholic, compares the transformation of the piggies to Christ's return: "It wasn't death," said Quim. "It was resurrection" (17.492).
It's worth remembering here that Card is a believing Mormon. It's also worth noting that Os Venerados, Novinha's parents who are on their way to being sainted, were killed by the Desacolada, just as Human is transformed by the Desacolada. The trees, which look over and watch the piggies, could be seen as saints of a kind, offering help to those left behind just as Os Venerados may help their people, human and piggie alike.