Who was King Lemuel? Was he Solomon?

The chapter names him twice: "The words of King Lemuel—the revelation which his mother taught him" (31:1), and "It is not for kings, Lemuel" (31:4). The name isn't anywhere else in the WEB. The book doesn't say who he was, where he was king, or when, and it doesn't name his mother. Solomon is named in the book's headings at 1:1, 10:1 and 25:1, and not in chapter 31. These notes add nothing to what the chapter says. The chapter also doesn't say where the mother's words end. The WEB's quotation marks close at 31:9, and the poem of 31:10-31 has no heading of its own; the introduction to Proverbs says the book doesn't settle whether the poem is still her teaching, and these notes don't either.