Please read my original comment more carefully. I never said that Solomon wrote Pr 31. I clearly stated that "Solomon wrote and/or
collected Proverbs and passed that wisdom along to his son(s)." Therefore, I never stated that Solomon wrote Pr 31.
As for King Lemuel, his identity has been much discussed, and some commentators believe that he was indeed Solomon.
They believe that Lemuel was possibly "a fond pretty name his mother Bathsheba gave him when young, and he thought fit to write it just as his mother spoke it; as mothers often do give such broken names to their children in fond affection to them: or it was another name of his." (quote from Gill's Exposition of the Bible).
Other don't think that Solomon was Lemuel. He has also been identified (by the Rabbinical commentators) with Hezekiah. It is possible that the name is a fanciful title to represent any virtuous king, invented for the purpose of conveying certain maxims. (Hastings Dictionary of the Bible).
Lemuel - Hastings' Dictionary of the Bible - Dictionaries - StudyLight.org
Anyway, we can't know for sure who King Lemuel was. That's why I intentionally stated that Solomon wrote and/or
collected Proverbs. Proverbs 31 being one that he possibly
collected.
I understand about being a stickler. I'm kinda one too.