As a noun meaning "native or citizen of the island of Lesbos," Lesbian has been used in English as a noun since the earliest translations of Herodotus and Thucydides. As a result, the notion of using lesbian as a noun when the later meaning of "a woman who is a homosexual" (Merriam-Webster's current definition) arose, around 1890, would not have struck many hearers as being a startling innovation. Interestingly, MW reports that both the noun lesbian and the noun sapphism (meaning "lesbianism") around 1890.
Though Sappho was well known to have been a native of Lesbos, one eighteenth-century makes no reference to her in expressing an unflattering opinion as to the licentiousness of the island's population (most particularly the men). From An Universal History, from the Earliest Account of Time to the Present, volume 3 (1738):
As to the morals of the ancient Lesbians, we cannot say any thing in their commendation ; they were given to all sorts of lewdness and debauchery, insomuch that to express the lewd and dissolute life of a debauchee, the antients used to say, that he lived like a Lesbian. [Hubert] Goltzius exhibits a medal [coin], which does no great honour to the Lesbian women.
I haven't found a picture of Goltzius's medal online; but another author observes that the medals of Lesbos were notably oriented toward sexuality. From Richard Knight, The Worship of Priapus and Its Connection with the Mystic Theology of the Ancients (1865):
It appears, too, that the act of generation was a sort of sacrament in the island of Lesbos ; for the device on its medals (which in the Greek republics had always some relation to religion) is as explicit as forms can make it.
One early English discussion of the immorality of Lesbos's inhabitants is Lodowick Lloyd, The Marrow of History; Or, a Looking-Glass for Kings and Princes. After making various scurrilous accusations against the people of Arabia and Babylonia (chiefly in connection with their supposed inclination toward incest), Lloyd turns his attention to "the Lesbians and the Sybarites":
With the Arabians and Babylonians, we may well compare the Lesbians and the Sybarites, people passing in that wickednesse, given to nothing but to sleep and venery, insomuch that they weary themselves with all kind of pleasures, and the excesse of their banquets, and the knavery of their women was such that made all the beholders to muse, and wonder at their excesse, as well in cloathing as in feeding, wherein they took glory : they expelled all sound and noise that might trouble their sleep. So filthy were these nations, that hand, foot, head and all parts of the body were naturally given to pollute themselves with venery.
William Guthrie, A New Geographical, Historical, and Commercial Grammar (1815) recounts Lesbos's past and continuing claims to fame:
It produces excellent oil and wine, the latter of which was anciently in high esteem, and still sells at a great price. It is famous for having been the native place of Sappho. The ancient Lesbians were accused of dissolute manners, and the modern inhabitants, it is said, too much resemble them in this respect.
And Julius Rosenbaum, The Plague of Lust: Being a History of Venereal Disease in Classical Antiquity (1901) reports that "irrumation" (oral sex performed on a man) was associated in ancient Greece with the island of Lesbos:
This the Greeks called λεσβιαζειν (to follow the Lesbian mode), because the vice was especially practiced by the Lesbian women, though in common with all others of the sort of the sort it came originally from Asia.
The idea that Sappho was amorously and perhaps sexually involved with other women was widely discussed among scholars in the eighteenth century, as we see in this passage from The Dictionary Historical and Critical of Mr. Peter Bayle, volume 5, second edition (1738):
People were so persuaded in Ovid's time, that Sappho loved women as men do ; that he makes no difficulty of introducing her making a sacrifice to Phaon [the young man in despair of whose indifference she supposedly cast herself into the sea] of the female companions of her debauchery.
No more the Lesbian dames my passion move,
Once the dear objects of my guilty love ;
All other loves are lost in only thine;
Ah, youth ungrateful to a flame like mine!
. . . . . . . . . . . . . .
Ye Lesbian virgins, and ye Lesbian dames,
Themes of my verse, and objects of my flames ;
No more your groves with my glad songs shall ring,
No more these hands shall touch the trembling string. [—Pope's translation]
Horace is another evidence against her in the complaints he supposes she made of the maids of Lesbos ;
And Sappho, in AEolian strains,
Who of the Lesbian maids complains.
for if she had reason to complain that the ladies of her country envied her merit, she would not have chosen the young ones for the subject of her complaint : but because she spoke to them of love, and the greatest part of them were either to simple, or, to speak better, to crafty to be catched, and those who had complied, had made her imfamous ; for this reason she complained of the young maids.
Although this translation of Bayle's dictionary is dated 1738, the dictionary was first published (in French editions) in 1697 and 1709; the first English translation appeared in 1709. In his entry for Lesbos, Bayle alludes to a certain abominable invention of the islanders:
There is an invention ascribed to the Lesbians, which is so abominable, that it is not fit to express it in English {C}.
So instead of expressing it in English [or French], Bayle devotes a very lengthy footnote to it that resorts to Latin quotations at various strategic moments:
{C} I shall not only forbear to explain it in English, but I shall even omit some parts of the Latin passages, which very grave authors did not scriple to write down at length in their books, with a design to give us some notion of that horrid practice. But since the great Erasmus did not think himself under any obligations to omit, in his Collection of Proverbs, that particular one to which that gave rise, I ought to be allowed the liberty of transcribing some of his observations. Aiunt, says he, (7), turpitudinem quae per os peragitur, fellationis opinor, aut irrumationis, primum, a Lesbiis authoribus fuisle prosectam, & apud illos primum omnium faeminam tale quiddam passam esse. [According to Google translate: "They say that the obscenity which is performed through the mouth, I think fellation, or incest, was first pursued by the authors of the Lesbians, and that among them the first of all women suffered such a thing."] ... Galen mentioned the Lesbian abomination, but without explaining what it was. He did not think it necessary at a time, when all the world understood that expression : but after several ages an infinite number of Greec words are become very hard to be understood, and the critics have been obliged to toil and sweat very much in order to guess at the meaning of the antients. ... I have omitted some words and some passages in this [lengthy but omitted Latin] quotation from Mercurialis : not that I would pretend this learned Physician had no right to relate all that he relates. A commentator or an expositor, who quotes only th authority of such a writer as Martial, who is well known to all the learned, cannot be blamed. We must either destroy all the antient authors, or e must suffer that their words be quoted, in order to find out and explain the sense of some difficult expressions. And yet I would not transcribe all the passages quoted by Mercurialis ; we ought sometimes to pay a regard to those scruples which are in fashion.
Still, the connection between Sappho and the modern sense of lesbianism appears not to have been universally recognized even in the nineteenth century. A typical presentation of the Sappho–Phaon episode appears in Agnes Smith, Olympus and Its Inhabitants (1851):
The most celebrated victim of this extravagant superstition [that diving off a promontory on the island of Leucadia into the sea would cure one of unhappy memories of a lost love] was the fair Lesbian Sappho, whose immortal verses so well depict the passion which destroyed her. Its object, a beautiful youth of Mitylene, was a man insensible to the charms of mind or the power of genius, he despised her unsolicited love, and, unable either to conquer it or to bear its torments, she sought its remedy in the waters of Leucos.
Here Sappho's heterosexual attraction to Phaon is front and center.
On the other hand, William Mure, A Critical History of the Language and Literature of Antient Greece, volume 3 (1854) alludes to the sexual attraction of women to other women in connection with "the Lesbian vice":
Another delicate question involved in this inquiry, is that concerning the precise nature of the intercourse between Sappho and her female associates. It will neither be necessary nor agreeable here to dwell at any length on the chapter of Greek scandalous history with which this question connects itself, further than by remarking that the taste for impure intercourse, which forms so foul a blot on the Greek national character, was not confined to the male sex ; and that, among the females who had the chief credit of being infected with that taste, the Lesbians were so remarkable, as to have procured for it, under its several varieties, the distinctive title of the Lesbian vice. This certainly affords strong presumption that in a Lesbian female association, the main object of which was the pursuit of love and pleasure, even this eccentric variety of the passion was not likely to be excluded.
...
We may add, what is probably known to most men who have lived much in the world during the last half century, that, at different epochs of that period, the "Lesbian vice" has not only prevailed to a greater or less extent in certain European capitals, but has, in almost every such instance, numbered among its votaries females distinguished for refinement of manners and elegant accomplishments.
Mure's Appendix F, dedicated to a discussion of "the Lesbian vice," is especially interesting because in it he makes clear that his focus there is not on what Rosenbaum in 1901 calls "the Lesbian mode" of sexual interaction between men and women.
That early commentators on the meaning of "the Lesbian vice" or "the Lesbian disorder" were not talking about a sexual activity limited to women should be evident from the following excerpt and footnote from a 1781 translation of Lucian's "Apophras":
With so many and such great names as these belonging to you, why should you be ashamed of Apophras only? How feel you, when even the common people say you have got the *Lesbian and Phoenician disorder? But perhaps you are ignorant of this too, or imagine that they mean to pay you a compliment by it, or are these well known and familiar to you, and Apophras alone blotted out of your catalogue? I am sufficiently revenged of you, even the women, it seems, know your character ; for, but the other day, when you wanted to get you wife at Cyzicus, the woman, who was well acquainted with your pranks, said, "I shall hardly take one for a husband who seems to want a husband himself."
- Lesbian. The Lesbians and Phoenicians were remarkably guilty guilty of a certain horrid and unnatural crime, which the Greeks very properly styled αρρητον μιξιν, a connection not fit to be mentioned, and yet it was universally practised.
The earliest unmistakable instance of "a lesbian" in the modern sense of the term that a Google Books search returns is from Edgar Saltus, The Imperial Orgy: An Account of the Tsars from the First to the Last (1920):
Indulgent and cruel, prodigal and mean, a woman in whom every contradiction was resumed, Catherine was an empress who made enormous an empire already vast ; a tsarista who enumerated her victories and could not count her amours ; a conqueror who had Adonis for secretary of the treasury and Apollo for minister of war ; a cynic who slaughtered Poland and called herself a pupil of Voltaire ; a sovereign before whom the entire pageant of passion and glory unrolled ; a tyrant and a lesbian who passed through history dripping with blood and exhaling the perfume of Eros.
This is, of course, much later than the earliest citation in Merriam-Webster, and is undoubtedly a sign of the limitations of the Google Books database or search engine or both. The earliest Google Books match for lesbians is from Jacobus X, Crossways of Sex: A Study in Eroto-pathology, volume 2 (1904), which devotes a lengthy chapter to "Lesbians, Tribades, Fricarelles, and Saphists."