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 is Eddie Joseph's “Confusingly Simple” from More Dumbfounders with Cards, 1951, p. 15. This topsy-turvy false shuffle leaves all the cards but the first pushed-off group facing the same way, and also retains the order of the whole deck. (It was reinvented by Jerry Andrus, who published it as “Drunken False Shuffle” in Andrus Deals You In, 1956, p. 91.)