I have seen them in several antique photographs, and the captions have included "lesbian" or "a cheeky reference to lesbianism," but I cannot find any other suggestion of this on the internet. The photos do appear to be erotic or romantic in nature and include only females.
Apologies if this isn't detailed enough, that's basically all I have to go on. Here is one example, but I've seen other photographs and even bought one.
Do you have other visual examples specific of lesbian affairs?
The term "spoon" to describe lesbian relationships is found in Havelock Ellis' Studies in the Psychology of Sex, Volume 2 (1900), where he cites "a lady who is familiar with an English girls' college of very modern type".
As far as I have been able to find out, these attachments—which have their own local names, e.g., 'raves,' 'spoons,' etc.—are comparatively rare in the smaller private schools, and totally absent among girls of the poorer class attending Board and National schools, perhaps because they mix more freely with the opposite sex.
However, "spoons", or "pair of spoons", seem to have been a colloquial way to describe lovers in American and British English of that period. The two ladies in the picture were probably American since the photo is from an American collection, so the "spoons" may refer to that expression and symbolize indeed their relationship, without "spoon" being specifically related to lesbianism.
Here are a few examples of the use of "spoons" to describe lovers.
They always were a making love, just like a pair of spoons, Hall the mornings, hall the hevenings, and hall the Hafternoons.
An Historical Sketch, Guide Book, and Prospectus of Cushing's Island, 1886
From the fleet of small boats ever in waiting at the boat-house you can select a craft commodious enough for your party, or of gondola proportions for "a pair of spoons".
When they were young and unmarried, they would walk along the beach on moonlight nights, or be discovered at evening parties in out-of-the-way corners, their friends would say that they were a pair of spoons.
A clothespin dressed in tissue paper to represent a fashionable young lady will illustrate a "heartless maiden," and two love-lorn faces painted on a couple of tin spoons will be immediately recognized as a pair of spoons.
Century Illustrated Monthly Magazine, 1892-1893
The Ballade of the Spoons
Still to your ears may Memory play
The tender old love-tunes,
And to life's end may you, I pray,
Be still — a pair of spoons
Demorest's Family Magazine, 1890-1891
"A Pair of Spoons" served for two tableaux representing the male and female flirts of party, who never could resist "casting sheep's eyes" at one of the opposite sex.
The Young Ladies' Journal, October 1, 1892
They strolled through the rooms, keeping clear, as yet, of the lately added pictures, and took possession of a bench in the most unattractive room into which a few bourgeois sort of people strayed in and out, who gave the aristocratic people a stare, and of course, thought them a pair of "spoons", as both were aware, with much amusement.