I thought I had found two examples of honor killing in ancient literature, although people online have disagreed with me.
In Livy, the killing of Verginia by her father Verginius in ancient Rome might have been fictional, but was probably at least based on events that had actually occurred. So the issue would be whether when something like the Verginius episode did happen, it fits the modern definition of honor killing.
Whether or not the Odyssey is fictional, would an event like Telemachus's killing of the woman slaves who were disloyal to Odysseus be considered an honor killing? (Telemachus does give his "honor" as a reason for hanging them rather than killing them with a sword).
Also, there's at least one other kind of honor killing in modern times: the killing of a family member who rejects the family religion. Is there any example of this in ancient history as well?