In Where the Lilies Bloom, why did the Luthers have to move?    

This is a very interesting question, because if we examine the Luthers and the way in which their situation deterioriates, we can see that gradually there is a move away from a civilised life towards a more primitive existence that makes them more exposed in every sense. Although initially they are able to remain in their house, in winter, the roof falls in, leaving them with a massive hole in the middle of the house which gives the weather and animals a chance to enter. Finally, near the end of the book, as your question tells us, the Luthers suffer such poverty that they are forced to move from their shack into a cave. The text describes them as being like "troglodytes," who are little goblin-like creatures who live in caves.

Although the situation that the Luther children confront is clearly dire, the text uses this gradual slide towards primitivism to suggest a link between the children and a closeness to nature. Throughout all of their struggles, however, the children manage to survive, and even, at stages, thrive, showing the indomitable human spirit in the face of crushing poverty.