The "lie" in this text which has everything to do with the relationships between the indigenous people of America and the whites who came and took their land and engaged in a process of trying to eradicate their culture is presented to the reader when Tayo discovers that his uncle's cattle had actually been stolen by the white rancher, Floyd Lee. Note what the narrator tells us about the lie that Tayo and all Native American people had been taught:
He knew then he had learned the lie by heart--the lie which they had wanted him to learn: only brown-skinned people were thieves....The liars had fooled everyone, white people and Indians alike... Their lies would destroy this world.
The lie then in this text refers to the way that whites, through their dominant education system and cultural supremacy, had tried to instruct and teach the Native Americans lies concerning their identity. The dominant discourse argued that it was only Native Americans who stole and robbed from hard working whites. Tayo discovers a very different reality, and the rest of the book represents his struggle to unlearn and relearn certain essential facts about the reality of life and how dominant white culture presents Native Americans, and how this compares with the reality of how they actually are. The final line of the above quote is significant because it indicates the power of lies, and how they can "destroy the world" through their ability to convince people of the so-called "truth" of issues, even when those "truths" are based on lies at their core.