Biblical Context:
The practice of casting lots for the goats is primarily associated with the Day of Atonement, or Yom Kippur, as described in the Old Testament. This sacred ritual is detailed in Leviticus 16, where God instructs Moses and Aaron on the procedures for the annual atonement for the sins of the Israelites.

Scriptural Reference:
Leviticus 16:7-10 provides the specific instructions: "Then he shall take the two goats and present them before the LORD at the entrance to the Tent of Meeting. And Aaron shall cast lots for the two goats—one lot for the LORD and the other for the scapegoat. Aaron shall present the goat chosen by lot for the LORD and sacrifice it as a sin offering. But the goat chosen by lot as the scapegoat shall be presented alive before the LORD to make atonement by sending it into the wilderness as a scapegoat."

Theological Significance:
The casting of lots in this context is a divinely ordained method to determine the distinct roles of the two goats. One goat is designated for the LORD and is sacrificed as a sin offering, symbolizing the payment for the people's sins. The other, known as the scapegoat, is sent into the wilderness, symbolically carrying away the sins of the community. This dual action represents both propitiation and expiation, key components of atonement theology.

Symbolism and Typology:
From a typological perspective, the casting of lots and the subsequent roles of the goats foreshadow the ultimate atonement through Jesus Christ. The sacrificed goat prefigures Christ's sacrificial death, while the scapegoat represents the removal of sin, as Christ bore the sins of humanity and removed them "as far as the east is from the west" (Psalm 103:12).

Cultural and Historical Context:
In ancient Israel, casting lots was a common practice used to discern God's will in various decisions, reflecting a belief in divine sovereignty over chance. The Urim and Thummim, sacred lots used by the high priest, are another example of this practice. The use of lots ensured that the decision was not influenced by human bias, emphasizing the sacredness and impartiality of the ritual.

Practical Application:
For contemporary believers, the casting of lots for the goats serves as a reminder of the seriousness of sin and the necessity of atonement. It underscores the holiness of God and the need for a mediator, ultimately fulfilled in Jesus Christ. The ritual also highlights the importance of seeking God's will in decision-making, trusting in His providence and guidance.

Conclusion:
The practice of casting lots for the goats on the Day of Atonement is a profound illustration of God's provision for sin and His desire for reconciliation with His people. It points to the greater reality of redemption through Christ, inviting believers to reflect on the depth of God's mercy and the completeness of His salvation plan.