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The phrase lust at first sight designates an instant, strong sexual desire for someone whom one has never previously seen.

It is a humorous variant of the older phrase love at first sight, which designates the fact of falling instantly in love with someone whom one has never previously seen.

While the latter phrase refers to an intense feeling of romantic attachment, the former phrase refers to sexual desire as a physiological instinct.

These are, in chronological order, the earliest occurrences of the phrase lust at first sight that I have found:

1-: From Beaumont, the Dramatist. A Portrait. With some account of his circle, Elizabethan and Jacobean, and of his association with John Fletcher (New York City: The Century Co., 1914), by the U.S. professor of English Charles Mills Gayley (1858-1932) [chapter 25, page 333]—the following is about The Coxcombe (first published in 1647), by the English playwrights Francis Beaumont (1584-1616) and John Fletcher (1579-1625):

We have a revelation of lust at first sight on the part of the husband’s friend, Mercury, of unnatural friendly pandering on the part of that ‘natural fool’ the husband, Antonio, and of easy acquiescence on the part of Maria, the wife, in the cuckolding of her idiotic coxcomb, who with the wool pulled over his eyes takes her back believing that she is innocent.

2-: From Notes of a study of the preliminary chapters of the Mahabharata. Being an attempt to separate genuine from spurious matter (Madras: Printed by V. Ramaswami Sastrulu & Sons, 1922), by V. Venkatachellam Iyer [Book 1, chapter 2, page 21]:

The account of Uparicharavasu is a solar myth, rather transparent in character. The compilers have mangaged [sic] to connect him, in a remote and perhaps left-handed way, with the Pandus and Kurus. This episode is found in the Calcutta edition as Chapter 63. In it is found the great event of Vyasa’s birth, as the result of love or rather lust at first sight.

3-: From The Sun Field (New York City: G. P. Putnam’s Sons, 1923), by the U.S. journalist and author Heywood Broun (1888-1939) [page 89]:
—Note: This novel, and the reviews it received, may have popularised the phrase lust at first sight (cf., below, quotations 4, 5 & 6):

“On the whole it stands as the finest play anybody’s ever written about lust at first sight.”

4-: From a review of Heywood Broun’s The Sun Field, by John V. A. Weaver, published in the Brooklyn Daily Eagle (Brooklyn, New York, USA) of Saturday 20^th October 1923 [page 3, column 2]:

Oh—the story—yes. It’s all about a ball-player of Ruthian prowess and Apollan appeal, for whom the lady editor of some thoughtful magazine such as the New Republic is smitten with what Mr. Broun calls “lust at first sight.”

5-: From a review of Heywood Broun’s The Sun Field, published in the St. Louis Post-Dispatch (St. Louis, Missouri, USA) of Saturday 24^th November 1923 [page 5, column 3]:

When Judith Winthrop, highbrow contributor to “Tomorrow,” a journal devoted to hyper-super thought and to the emancipation of the earth from ordinary things, saw Tiny Tyler, outfielder of the Yankees, make a great catch, it was “lust at first sight” for her, we are told by Mr. Broun.

6-: From the column It Seems to Me, by Heywood Broun, published in the Springfield Evening Union (Springfield, Massachusetts, USA) of Saturday 29^th December 1923 [page 6, column 6]:

Some protective league is needed to guard authors from being compelled to shoulder the sins of their characters. Traveling salesmen are not alone in dashing right past quotation marks to get at innocent authors. Only the other day we received a clipping from a Newark newspaper containing a review of “The Sun Field.” Naturally we expected a slam, because as a rule people don’t bother to send you reviews unless they are unfavorable. And it seemed to us entirely reasonable that the critic should begin, “Heywood Broun makes me sick.” But the specific reason assigned for this nausea seemed to us unjust. “He says,” continued the reviewer, “that love at first sight is actually lust at first sight.”
Now, we never said anything of the sort, but the heroine in “The Sun Field” did say something to that effect. Why should we be blamed for that? People in books have all sorts of notions. Even with the best will in the world the author can’t do anything to pacify them and bring them around to his way of thinking.

7-: From a review of White Cargo, a stage-play by the British playwright and screenwriter Leon Gordon (1894-1960), which opened at the Orpheum, Nashville, on Friday 20^th March 1925—review by Ralph McGill, published in the Nashville Banner (Nashville, Tennessee, USA) of Saturday 21^st March 1925 [page 3, column 4]:

For publicity reasons, we suppose, the play has been advertised as “Love in the Tropics.” It isn’t that at all. There isn’t one tiny bit of love in it. There is lust at first sight, but no love at first sight. There are tropics and tropics, and the west coast of Africa is a different tropic from that of the south seas, though we suspect that the lust at first sight holds good in all of them.

8-: From The Middle Country Road, a short story published in The Romany Stain (New York City: Doubleday, Page & Co., 1926), by the U.S. journalist and author Christopher Morley (1890-1957) [page 246]:

In the case of the novel that D— M— and I wrote we ruled out all philosophizing; the narrative (if I do have to say it, because the publisher never did) was delightfully rapid. This was because the story was written with the firm intention of selling it to the movies; which has not yet been consummated. The agent complained that it did not have enough Lust at First Sight.