The legal principle described as life for life is known as lex talionis (“law of retaliation”). This means the punishment must match the crime (see Exodus 21:23; Leviticus 24:20). It should not be too weak or too harsh.
Appropriate punishment is a necessary function of government (compare Romans 13:1–7). It helped maintain Israel’s spiritual integrity as God’s people (see study note on Deuteronomy 17:7).
But vengeance belongs to God, not individuals (see 1 Samuel 25:26, 33; Matthew 5:38–39; 1 Corinthians 6:1–8).