The final word, κυρίου, “Lord,” modifies both παιδεία and νουθεσία. The reference is to Christ who is their Lord. In other words, the father’s training and admonition is not to be anthropocentric as it was in Hellenism nor centered around the law as in the rabbinics but, rather, Christocentric… that the training and admonition come from the Lord or are prescribed by the Lord through fathers. The fathers are the Lord’s agents and, therefore, raise their children according to his mandates. Such training and admonition would be sensitive to the children’s responses and needs.
Ephesians, An exegetical commentary