This face-up, face-down shuffle ploy of Sid Lorraine's was published as “The S. L. Reversed Card” in John Braun and Stewart Judah's Subtle Problems You Will Do, 1937, p. 34.
Braun and Judah noted in their introduction to Lorraine's trick: “The reversed card trick we present here was originated by Sid some years ago, and one or two variations of the principle employed have appeared since then.” This discreet mention seems directed toward R. W. Hull's “Topsy Turvy Cards” in his booklet Eye-Openers, 1932, p. 10. Hull's face-up-face-down shuffle differs in its outward actions from Lorraine's but delivers the same result of the deck consisting of back-to-back halves. Hull preceded this shuffle with a demonstration of a legitimate, similar-looking mix, after which he openly righted the cards before doing his false topsy-turvy shuffle.
Another notable variant, published years after Lorraine's shuffle and Hull's variant, is Jerry Andrus's “Drunken False Shuffle” from Andrus Deals You In, 1956, p. 91. This topsy-turvy false shuffle leaves all the cards but one facing the same way.