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.
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 i 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 connection between Sappho and the modern sense of lesbianism appears not to have been universally recognized in the nineteenth century. From 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.
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 discussion in an appendix 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.
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."