The words, &c. The Hebrew dibrey has no governing noun; so one must be understood thus. "[An unnamed one's] words [addressed] to king Lemuel:. burden which his mother [repeatedly] taught him".
king Lemuel. to El and for El,. king. Compare Jedidiah. beloved of Jah (2 Samuel 12:25). Solomon was the royal seed in the line of Him Who is King of kings and Lord of lords. The Talmud says (Avoth d'Rab. Nathan, c. 39): "Solomon was called by six names: Solomon, Jedidiah, Koheleth, Son of Jakeh, Agur, and Lemuel".
prophecy. oracle, oracular utterance, or burden.
his mother. Compare the Structure, (p. 864).