Lucas's allegory
Lucas's story is a perfect allegory for the one of the main dilemmas of the collection. How can white people own black people as slaves? Lucas hates himself and who he really is, since he knows privately that his grandfather was black. However instead of using this knowledge to see that his culture is broken, Lucas spends his life desperately searching for wealth and praying no one finds out his secret. For his cowardly ways and his desire for power, Faulkner rewards him accordingly: His wife leaves him alone in his shame.
Isaac's Messianic allegory
Isaac's name and story are both strong indications that he is to be viewed as the story's "Messiah figure," which simply means that the character's life and the decisions he makes all look strikingly similar to the Jewish Messiah narrative (obviously, Jesus Christ would be a good case study to compare him to). Isaac's name is an allusion to the Biblical character Isaac who is literally Jesus's ancestor. Like Jesus, the Biblical Isaac is defined by his sacrifice.
In Isaac McCaslin's life, he also serves a prophetic or messianic role by sacrificing his worldly inheritance. This doesn't mean that he hates his family, but rather, it means that he feels their ways are corrupted, and he will not participate in their hateful, power-hungry games of property-ownership and slavery. Because he makes that serious sacrifice, he is the "hero" of the story, and Faulkner rewards him in the story, "Autumn Delta."
The symbolic encounter with "Grandfather"
In the story titled "The Old People" a young Isaac encounters a deer spirit after he kills his first deer. The Native American mentor who is helping Isaac tells Isaac that the deer spirit was "Grandfather." The meaning here is in the name. By naming the spirit "Grandfather," the Native American teaches Isaac that Isaac has more than one heritage. There is the involuntary heritage of his white family, and there is the heritage of his humanity itself, a kinsman with nature. Therefore, "Grandfather" represents unity with nature.
The motif of family
An obvious yet meaningful motif is the inclusion of various family members throughout the story. The reader is getting a broad view of society, since many of the characters are cousins and family, and since the town where the family lives is pretty small, and each family knows all the other families. It's as if the reader is seeing multiple facets of the same object, and each person of the family represents another relationship one might have toward one's family and identity.
The motif of death
Faulkner never was known for light-heartedness. These stories feature many deaths. In "The Pantaloon in Black," a black man is lynched by the KKK for murdering a white man. In "The Old People," a young boy takes an animal's life for the first time. In "Delta Autumn," that young man has become old and the symbolism indicates that he will die soon. In the final story, the title story of the collection, "Go Down, Moses," a man helps an old woman reclaim the body of her executed grandson. The motif of death doesn't really need to be interpreted; it represents actual human death.