Life-prolonging/life-extension therapies are now more-or-less a staple of science fiction, and do have a long pedigree. The two earliest stories I can recall that make use of them as a setting element are James Blish's Cities in Flight tetralogy (1950-1962), and Heinlein's Future History in 1941 (serialization of Methusaleh's Children). However, both of them seem to me to have the 'feel' of reusing an extant trope. Thus, the question: What's the earliest use of life-extension/life-prolonging therapies in SF?
So we set out walking along Calle Grande through a maelstrom of light and a chaos of noise. After a bit, we passed a tremendous building which was set back quite some way from the street and had a steel wall all around it. I asked Ruiz what it was.
"That, sir," he says, "is the Leopold Austriol Foundation. Leopold Austriol is a man one hundred seventy-seven years old; he is the richest man in Floreat Go-Lee; that building there, the Leopold Austriol Foundation, is a monument to his fear."
What was he afraid of, I asked.
"Sir," says Ruiz, "he is afraid of death."
I asked if he could escape death even in such a tremendous building.
"By gad, sir, he's doing it!" says Ruiz. "When the fear first came on him, he had that building erected and he had it outfitted with every subtle tool and device and compound and tincture known to the surgical and medical professions, and he had it manned with every outstanding member of those professions, and he went into it and ordered those he had hired to keep him alive. And, by gad, they have done so!"
"How long has he been there?" I asked.
"Seventy-nine years," says Ruiz. "The doctors have constructed a sort of glass case with tubes leading into it and out of it, and they have old Leopold enclosed in that case, and nothing can get into it without their scrutiny and sanction, nor can anything leave it, not even old Leopold's life-spark, without their permission. He has been in that case more than seven decades now, and he is confident of his own particular immortality, and so are the doctors who tend him. Those doctors are cunning devils—positive magicians with their metabolic machines. They feed old Leopold through one tube, drain him through a second, aerate him through a third. They keep a perpetual X-ray turned on him, one one of them is perpetually on watch for the first sign of worn tissue. When they note any, they operate on him in his glass case and substitute new tissue for what he has worn out. One day a week, the public is allowed in there to inspect the old man, and a while back I availed myself of the privilege. He hardly resembles a human being any more, appearing, instead, to be a sort of huge rolled-up beefsteak with all manner of gauges and thermostats and pipes stuck into it. But he's undoubtedly alive. There's no question about it."
"Why should the doctors take so much trouble with him?" I asked.
"Gad, sir," says Ruiz. "Why, it's on account of his money, of course. You don't think a Heilar-Wey doctor would fool with him for a minute if he had no money, do you? But he has matters arranged so that as long as they keep him alive they are paid unbelievably huge salaries and get bonuses, also. The moment he dies, though, all the salaries and bonuses automatically stop, and every cent of his fortune is to be used for constructing a magnificent tomb to perpetuate his name forever."
1929: "The Eternal Man", a short story by D. D. Sharp; first published in Science Wonder Stories, August 1929, available at the Internet Archive; reprinted in Startling Stories, January 1939, also available at the Internet Archive.
And then he discovered it. He did not need to prove the experiment by waiting and watching until the end of time to find out whether the cells would eventually die. He knew they would not die. A few drops of pale green fluid in the graduating glass in his hand would permit any man to live eternally. He knew this was possible for he had at last found the combination he sought; the chemical which continued life without the necessity of decay.
1899: "The Rejuvenation of Major Rathbone", a short story by Jack London, first published in Conkey's Home Journal, November 1899. Plot summary from Everett F. Bleiler's review in Science-Fiction: The Early Years:
Dover has invented a chemical means of rejuvenation, presumably in some way glandular. With some trepidation he and the narrator give a dose to moribund old Major Rathbone, a Civil War veteran. The treatment works exceedingly well. Rathbone is restored to his youth (though his hair and beard remain white), but with the irritability and crotchetiness of his old age. After a time it becomes impossible to control the major, who not only lives riotously, but wants to renew his commission to take part in the war against Spain. The two scientists are dismayed at the result of their experiment and wonder how to tone the major down. They finally rejuvenate an ancient flame of the major's; this takes his mind off the war.
Around 1890: Professor Schwarzbaum announces his great discovery at the Royal Institution. He has discovered a chemical means for preventing aging in the human body. It will not rejuvenate, but it promises to prolong life indefinitely.
A manuscript found in the drawer of an escritoire. The writer, who can remember events from the time of the Commonwealth and Cromwell, is tired of life and wishes to die. He reminisces about his past. His life was saved twice by an ancient man named Nureddin, who offered him an elixir to drink. This elixir, which is rejuvenating, healing, and age-arresting, is prepared from ordinary water by electrolysis and operates by keeping the blood vessels and other organs soft and unclogged. After a time, however, it reduces the density of flesh and bone, so that the partaker loses weight and becomes shadow-like and attenuated, capable of passing through walls. The immortal man has hecided to die and will not consume his elixir any longer.
1884: The Disk: A Tale of Two Passions, a novel by George A. Wall and Edward A. Robinson, available at Hathi Trust Digital Library. From Everett F. Bleiler's review in Science-Fiction: The Early Years:
He has discovered how to remove the perishable component from food, leaving food pure and far more healthy for humans than ordinary food. Even more, Alder has discovered that if he places a human in suspended animation by means of an injection and subjects the body to the cleansing gases he uses in his food processing, all diseases will be cured and the body will be perfect of its sort when revivified. This seems to promise, if not immortality, at least great longevity.
The narrator chances on the sole surviving copy of a small book written by Apollonius Septrio, a Renaissance magician-scientist who was burned as a sorcerer. In the book is a recipe for immortality, which amounts simply to eating a very common weed.
1799: St. Leon: A Tale of the Sixteenth Century, a novel by William Godwin, available at Project Gutenberg and the Internet Archive. From Everett F. Bleiler's review in Science-Fiction: The Early Years:
St. Leon, one of the lesser French nobility, by chance obtains the secret of making gold and an elixir of life. The process, which he received from a dying refugee whom he helped, seems to be chemical, without supernaturalism of any sort. What with wealth and youth, it would seem that St. Leon's problems are over, but this proves to be far from the case, mostly because of his weakness, arrogance, coldness, and selfishness. On achieving immortality, for example, he immediately scorns his devoted, helpful wife and children as insects of an hour and deserts them. In society, too, his promiscuous display of wealth renders him a temptation to the greedy authorities, and he is in and out of prison and political difficulties. All in all, instead of happiness, he has found misery.