The words of King Lemuel - מכך למואל דברי dibrey lemuel melech, "The words to Muel the king." So the Syriac; and so I think it should be read, the ל lamed being the article or preposition.
But who is Muel or Lemuel? Solomon, according to general opinion; and the mother here mentioned, Bath-sheba. I cannot receive these sayings; for
But, however this may be, there is no evidence whatever that Muel or Lemuel means Solomon; the chapter seems, to be much later than his time, and the several Chaldaisms which occur in the very opening of it are no mean proof of this. If Agur was not the author of it, it may be considered as another supplement to the book of Proverbs. Most certainly Solomon did not write it.
The prophecy that his mother taught him - משא massa may here signify the oracle; the subject that came by Divine inspiration; see on Proverbs 30:1; (note). From this and some other circumstances it is probable that both these chapters were written by the same author. Houbigant thinks that Massa here is the name of a place; and, therefore, translates, "The words of Lemuel, king of Massa, with which his mother instructed him."
That his mother taught him - Compare Proverbs 1:8; Proverbs 6:20. If we refer the chapter to Israelite authorship, we may remember the honor paid to the wisdom of Miriam, Deborah, and Huldah; if it was the honor paid to an Edomite or an Arabian, we may think of the Queen of Sheba, whose love of Wisdom led her to sit at the feet of the son of David.